What's his rank in the family after the Corleones leave to Nevada, he is Frank Pentangeli's right hand man, but is he still just a soldier? Also at the Senate hearing he says "At first, just like everyone else, I was a button man..." Meaning he was no longer one. Thoughts?

Welcome, Don Vincenzo!
I agree that "At first I was a button..." strongly implies that he was a lot more than that under Pentangeli. If Frankie was a caporegime under Michael, then Cicci probably was either a captain or his consigliere.

I assumed he was a capo under Pentangeli. Don't think Willie was consigliere material, but then again Frankie wasn't the sharpest knife in the drawer either.

Cicci to me would be more of an underboss, I agree he's not consigliere material, he was always more muscle or atleast that's how it appears in the moive. I always loved him for some reason as I've seen many on the board have felt the same feelings.

I suppose I actually should have asked this as well, what is Frank Pentangeli considered I know he is a capo under Michael, but is he considered a street boss in which Cicci could just be his right hand man and deliver orders through him, ect.?

Frankie would have to be a street boss since the Big Boss was treading streets considerably to the West of NYC.

This raises another question about Cicci: To whom did he belong at which time?
When Carlo gets his punishment from Sonny, Cicci is obviously kind of a bodyguard of Sonny.
Later he kills Stracci or Cuneo in the revolving door, which means he must be one of Rocco's, perhaps one of Clemenza's men.
If he was one of Clemenza's button men, then he was simply transferred to Pentangeli. But if he was under Rocco?

One of the things we have to keep in mind when trying to divine the answers to these questions is production values. Cicci was a character that FFC wanted high profile in scenes. So, he played him so. As a result, you can't connect the dots.

Yes. Cicci's really a minor character. But Joe Spinell was so perfect for the role that he gets mentioned here far out of proportion to his actual role in the film. FFC obviously valued his presence by giving him little cameos that gave him the visibility that seems to attract us here.

As for who he belonged to: We first see him in the scene where Michael is saying goodbye to Sonny before meeting Sol and Mac. Look in the background of that corridor and you'll see Tessio impatiently gesturing, then Cicci comes to him. That suggested to me that Cicci was with Tess originally. And yes, he's bodyguarding Sonny, and Sonny had his own regime, so... Then at the end, he says, "Sal, Tom, the boss says for you to go on ahead..." which could mean that he'd taken on some higher role in the family independent of Tess and Clem.
In the novel's denouement, Neri went with Michael to Nevada, and Rocco stayed with Clemenza in NYC. Cicci wasn't a character in the novel.

I suspect Cicci got a "battlefield promotion" after Tessio's betrayal, he shot one of the heads of the five families, and thn came to the mall with instructions to end Tesssio's plans to take Michael to Brooklyn, and to arrange for Tessio's last car trip.

Although he did not play a prominent part in the two movies, his acting was terrific, proving the old maxim, there are no small parts, just actors who play their parts small.

Could be, but again that could just be the way FFC directed. As far as the end goes, the novel says that Mike instructed Clemenza privately. So, Clemenza would have then instructed someone to perform the "go on ahead" role. He chose Cicci indicating that Cicci was part of his regime, but not necessarily.

By the way, not much is made in the novel or film of Sonny's regime. I wonder why. Why wouldn't Sonny use his regime to guard the mall after Vito is shot or, in any case, from day one?

Good point. Sonny may have alluded to his regime in The Godfather as follows:
When Clemenza comes into his apartment to say word on the street is Vito is already dead, Clemenza then asks Sonny if he should send any men to protect him and his family. Sonny tells him "no" probably because he suspected CLemenza may have had a hand in the shooting. Minutes later, however Sonny tells his wife that he is sending some men over to protect them. Those men were probably in his regime.

Sonny's "hundred button men" remark was stated emphatically and with pride. I'd assume he was speaking of his own regime in that instance.

Well, again the novel makes it clear that Sonny was trying to determine if Clemenza was a traitor by listening closely to his voice o the phone. The fact that Sonny tells Tessio to recruit men to guard the mall (in both the novel and filmsaga) confirms that. But, again, why do that when he has a regime? Why just have a couple of his people come to his house?

The 100 button men statement - I think that was a generic reference to his deployment of Corleone forces generally and not necessarily a reference to his own regime.