Before the shooting at Mikes house in part 2. Mike is always talking about his important business with roth and nobody can ruin it. What was this business and why was it so important?

Was it a stepping stone to go legit (unlikely but you never know).

Or buying the casinos in Havana to go bigger and more global (another greedy scheme).

Did he fully trust Roth before the shooting or was he suspicous of him before? as Frankie was complaining about Roth and the Rosoto Brothers.

His business with Roth was probably a potpourri of illegal activity most of which focused on the Cuban casinos. Since it was international and since it involved a partnership with a government and since it involved potentially huge profits, it was very important. Although it's not expressed in the movie, the Cuba connection was probably also important to drug trafficking.

No, I don't think it had anything to do with Michael's attempts to go legit which I don't think Michael had any intention to do.

All Mafia dons are supicious of everyone else in the business. There is only faux trust - there are only working relationships that end when it is convenient to end them. He had to work with Roth to achieve what he wanted to achieve.

In addition to what Olivant said:
Michael's probable intent was to define going "legitimate" as channeling the Corleones' dominant position in illegal gambling into dominance in the two places in the Western Hemisphere where gambling was legalized at that time: Nevada and Havana. Roth predominated there. The first deal we saw Michael involved in when he returned from Sicily was to try to buy out Moe Green, Roth's best friend, from his Vegas hotel; and when Moe said no, Michael had him killed. By the opening of GFII, Michael had moved the family HQ from NYC to Nevada, owned or controlled three hotels, was about to force Klingman from a fourth hotel that Roth partly owned.

I believe Roth knew all along that Michael's intent was to take over his entire gaming empire. So, Roth pretended to treat Michael as his son and heir-apparent, doling out little pieces of his empire--and stringing him along until he could find a way to have Michael killed. The "important business" was Roth seeming to give his Havana interests to Michael. That was the final piece--and the bottom of the trap that Roth had set for Michael.

Did Michael trust Roth? If you asked him, he'd say no--"it's business." But I believe that Michael was so obsessed with becoming "legitimate" (on his terms, under his definition) that he blinded himself to the obvious: Roth was stringing him along.

Olivant raises another point: a possible drug connection in Cuba. Though Roth was not identified in the film as a drugs guy, pre-Castro Havana (and other parts of the Caribbean) were centers for drug trafficking. If drugs were part of the deal, Michael would have been part of the drugs traffic--drugs go hand in hand with gambling.

Yep the drug channel of havana makes sense (possibly inspired by Luckys enerprise their in real life). Thanks for the answers Olivant and Turnbull.

It was mainly the casinos in Havana and they even discuss having the means to get a man elected President in the U.S so that eventually gambling would be legal in the States to further legitimize there $$$ and the family. "We're bigger than U.S Steel"