Tessio, Fredo, Carlo and Kay were the insiders of the family who betrayed. Ofcourse Kay's secret abortion is debatable. But it is ironic that Carlo and Kay, were more successful than Tessio and Fredo. The last 2 were mobsters by profession. What do you think were the resons behind this?

Fredo a mobster by profession? Don't think so! There is never mentioned that he has killed anyone, ever. He never became a bigshot in the Corleone family, he only was good enough to "pick somebody of the airport" of "run a Micky Mouse nightclub". I also think Fredo never meant to have Mike killed, the reason why he was trying to help Roth was because "there would be something in it for him".

Carlo ended up dead, and if it wasn't for him the Corleone family would end up with Santino as the Don. I don't know if that would be a succes, I think Vito couldn't have a better succesor then Mike.

Tessio didn't succeed indeed, but his betrayal was "strictly business", while Carlo betraying Sonny was as personal as it can be. Mike just outsmarted him.

Then Kay. Her abortion was the most personal thing possible she could do to Mike. She succeeded in that, but she barely saw her two children after that.

I think it just shows that if you're a mobster, you're dealt with more quickly, because it's more business then personal, but every traitor get's a punishment.

If Michael was supposed to obey the laws of his world strictly and without humanity, he had to kill Kay as other traitors. What she did was much worse than Fredo's guilt. She killed his own child mercilessly, and without any real reason except giving him pain, as much as possible, though he never did anything to cause her pain intentionally. She betrayed him and wished to separate him from his other children. And she wished to leave the organization which nobody leaves alive. As a former insider she well might see and know much, even unintentionally. And in her state of mind, thinking that if Mike would be imprisoned, the state could return her children to her, she might very well decide to testify against him to the FBI.
If after all he left her alive, it was an act of that very humanity that FFC denies him in part 2. And if he had qualities to act so, why should he kill Fredo, who was much closer to him by blood, and didn't even know what was he really doing!
Well, all FFC-composed sequeling stuff is full of logical holes, and this is one of them.

Kay wasn't even close to being a member of the organization.

How do you measure "success"? Carlo died, just like Tessio and Fredo. Kay lost her children to Michael and was thrown out of her house.

But she knew enough. As any insider. If she didn't participate, it didn't mean that she didn't know what was done, or guess at least. And she knew structure and people who were working for the Family. Rather valuable info!

No, I dont think she knew anything.First of all, after the end scene in Part 1, I dont think she wanted to know anything, and secondly, Mike, I believe, didnt tell her anything. The buttonmen and probably Fredo as well,didnt hang around and gossip with her, so she was probably in the dark, something she didnt have a problem with either.

I didn't mean successful as in escaping punishment. We know very well that Michael would not spare anyone. Poor Pentangeli was forced to suicide. Fabrizio, I am not sure, in some deleted scene, he is supposed to have been killed.

But carlo did get Sonny killed and Kay killed his son. No one suspected them before, michael could only react later. But Fredo's and Tessio's targets were Michael himself. Had they been more careful, there would be no michael to take revenge. (in a way Fredo also managed to escape suspicion, but was not smart enough to ensure a hit). People like Tom were buisiness men, they would not bother about vendetta.

Nobody's mentioning my favorite rat... Willie Cicci

Mista, Your favorite rat was just a button, not an insider who was close to the family. That is the reason I did not include fabrizio or Frankie in the original post. But you are welcome to discuss Willi's success in betraying michael

I think she knew many things without being told or gossiped with. Remember her talking to him in GF2 about legitimacy, while dancing?
Michael: Kay, I'm sorry about all the people today. Bad timing, it couldn't be helped, though.
Kay: It made me think of what you once told me - "in five years the Corleone Family will be completely legitimate." That was seven years ago.
Michael: I know. I'm trying, darling.
What could make Kay suspect he deceived her and talk about it while dancing? I think, seeing Ola and Frankie at the party. This shows that she knew who they were and what kind of business were they responsible for. And saying in GF 3 "You're still a liar" about his still having Al Neri might show that she knew wery well that he is a professional executioner and what he did for Mike before. But of course GF3 is no proof of anything, being void of logic in general. So I think she wanted to know as much as possible and kept her eyes open, and besides knew most of people working for the Family in face!

To add to Just Me's thought, Kay expressed surprise that she did not know about Frankie's brother. I gather that she must have known a lot about michael's business, eventhough michael might not have explicitly shared it with her. Connie knew about Carlo's murder and Kay knew about Fredo's murder. Only michael assumed otherwise.

Yes, Cicci was just a button. And he may even have tried to help Michael at the Senate hearing:

When asked by Senator Geary if he had ever received a direct order from Michael, he replied, "No, I never talked to him." In fact, he did. Recall that, near the end of GF, as Tessio was about to get into his car, Cicci says, "Sal, Tom, the boss says for you to go ahead and he'll come later." Sounds like he got a direct order from Michael that, in effect, made him an accessory to Tessio's murder.

Yes, so it sounds, but it doesn’t mean that he really had any direct order. Michael was clever enough not to give direct orders to buttonmen. In the book, Michael talks to Tom before that: “Send Clemenza in to me. I’ll instruct him personally. I don’t want to see Tessio at all. Just tell him I’ll be ready to go to the Barzini meeting with him in about half an hour. Clemenza’s people will take care of him after that.” So, Mike instructed Clemenza alone to take care of Tessio, he didn’t go into details, he didn’t care who exactly will be those “Clemenza’s people”, it was his (Clemenza’s) job to pick necessary number of bodyguards for Tessio’s transportation.
When in the beginning of the novel Sonny tells Clemenza to “take care” of Paulie Gatto, he also doesn’t tell him details, and Clemenza has to work out the plan himself. He needs to throw his victim off the track, and find an excuse for their trip together, so he invents a story: “Damn that Sonny… He’s already thinking of going to the mattresses. We have to find a place on the West Side.” Of course Sonny gave him no such order, but is it important what lies will he tell to the traitor who will die in a few hours?
So I believe it was with Ciccie. He never spoke to Michael, who might not know him at all - just another buttonman. But when Clemenza received his orders from Mike he had to organize everything so that Tessio wouldn’t suspect anything to the last, so that he couldn’t resist or run away. That’s why Tom goes to the kitchen as if nothing happened and says to Tessio that Mike is ready and he’d better make his call. Tessio is at ease, he calls and they exit the Don's house to go to Michael’s. If there were many bodyguards waiting for them, it might awake his suspicions, so they were met at the doors of Mike’s house by “one of the bodyguards”, who told them “boss says he’ll come on a separate car”. Mike had nothing to do with it, but it was necessary to stop them there, outside the house, where the car was waiting for them, and more people hidden. When Tessio says, “He can’t do that!” - “Three more bodyguards materialized around them”. Now Tessio had no chance to escape, and Tom could safely say “I can’t go with you either, Tessio.”
It’s clear that this entire situation was carefully prepared and directed by Clemenza, and perhaps that line was his idea, and he told the bodyguard what to say. Michael might really never talk to Ciccie.

If Santino wasn't so headstrong, and listened to Thomas Hagen, he could become an excellent Don.

Yes, that's how it went in the novel. But Cicci is a creature of the films. And so I'm going by what he said in the two films in which he appeared.
For the record: I agree with you that Michael would have been violating a cardinal rule to have given a direct order to a button that could have implicated him in a murder. But again, I'm going by what Cicci said in GF when he ushered Tessio into the car, and at the Senate hearing.

Yes, he said it, I didn't mean to contradict the fact that he said "boss says" to Tessio in the movie as well as in the book. I only meant that his saying so doesn't mean at all that it was really said by Michael. It might be lie, and had to be lie, as was the common practice. It might be directed by anyone who headed the operation, and it was said only to stop Tessio at the spot. He was not under oath saying it.

One thing about the Godfather is that the book differentiates from the movie. So in the film Cicci ha dto have gotten the order from Mike to kill Tessio.

I don't quite get your logic, why if movie and book differ sometimes, it must mean that Cicci "had to have gotten the order from Mike to kill Tessio" in this particular scene. (BTW, it is never showed or said in either that Cicci was the actual killer.) They differ in some things, but mostly movie is done very close to the text, and this scene with Tessio and bodyguards is carefully made almost word-to-word from the book. If the scene between Mike and Tom is missing, it doesn't change much.
More than that, even if we talk about the movie alone, I can't see any particular reason why he "had to have gotten the order from Mike".
1. The aim of Ciccie's appearance on their way was to stop them on the spot in front of Michael's house, so that they wouldn't enter it. To prevent it he had to say something, and it could be anything whatever, any lie that could stop them for a moment. It was not really significant what he would say.
2. Cicci might not be the author of this phrase. "Boss says", after all, doesn't mean "Boss said to me". The phrase might be passed to him by Clemenza, or Rocco, or Neri, or anyone else who headed and organized the operation.
3. He could not possibly talk to Michael because Michael was clever enough not to talk with his buttonmen directly. Besides, there were strict rules for Don's safety. If he gave such order, there always had to be a buffer, and even if it wasn't Clemenza, as we don't see him around in the movie, it had to be Hagen, he seemed to be in charge and it was he who had to call Tessio from the kitchen.
4. He could not get the order from Mike because the operation, even the transportation of T. involved several other buttonmen and had to be planned and arranged by someone superior to them. Being just a button, he was in no way the planner of it, and surely you don't mean that Mike was going around and instructing every buttonman personally.
These are my reasons to think that his phrase was just an eligible lie.