If “Michael gave up on Cuba for good while he was in Havana” ie: not before his arrival [after the Tahoe shooting] why turn up without the $2 million though

It seems apart from Fredo nooneelse knew that Michael had figured out it was Roth who tried to kill Michael in his home unless the ever astute Roth was covering all the bases with his birthday speech alibi for Michael's 'unfortunate political' death

Michael was hanging around at the New Year's Eve party probably as he had to be seen being the host, for Geary and the government people, having a good time, Fredo's specialty!

However if Michael had accepted Cuba was a lost cause / "Just want to wait" and “Hyman Roth will never see the New Year” hanging around in Roth's stronghold was too risky even to “find out who the traitor was in his family”

If Geary had not asked Fredo, how Fredo found the superman club and Fredo had not slipped up, Michael would have been none the wiser as to who the traitor was in his family
Concede the slip up did happen, nevertheless how did Michael envisage he could find out who the traitor was in his family? Bussetta threatening Ola with a coat hanger?!

As regards the carving up of Roth's empire, my misunderstanding – I inferred from Roth's birthday speech that Roth was 'anointing' Michael as the future Roth, the boss having control and making money for the partners