Welcome, NIAFmember! You're not the only one who's asked those questions--they're among the most often-asked on this Board. You can find the answers to these and to others by using the Search utility here. But, briefly:
1. Michael tells Tom that he's out because he's "not a wartime consigliere."--he didn't have the cunning, or perhaps the force, to function during wartime as his predecessor, Genco Abbandando, did. That's a very truncated answer. Search that topic and you'll find many interesting nuances.
2. Michael was a master manipulator. The finger of suspicion was pointing at Pentangeli for the Tahoe shooting. Michael was almost totally convinced it wasn't Pentangeli. But he yelled, then asked for his help, to soften him up--to make him so grateful that Michael didn't blame him that he'd agree to Michael's request to "settle these problems with the Rosato brothers." He played Frankie like a violin.
3. The Rosatos were a faction in Clemenza's family. Pentangeli inherited them, and the alleged promises Clemenza made to them for territories. They are based on the real-life Gallo brothers, a faction in the Profaci family in NYC. The garrotting of Frankie is based on an episode in the Gallo/Profaci war.