I think Jaime will stay away from Cersei... but one day Cersei will miss Jaime so much that she will do what ever it takes to get him back - even if it means that the rest of the world will know about their twincest... and for that they will be killed.
As for Myrcella and Tommen: I think Tommen will stay king quite a long time - right until Jaime and Cersei die. When he learns the truth, he will give the throne up and survive.
Myrcella will probably be the victim of the players' game of thrones and die... or end up having to flee from Westeros with her brother Tommen when Cersei and Jaime die.
Tyrion. Gosh I don't know where to begin. He will somehow escape all that people we know because everybody wants to kill him and he then decides it's time to follow his own dream... which is to find Tysha, and through Tyrion we will see lots of cities like Asshai. Somewhere he will find Tysha, realize that Tysha never loved him and isolate himself for the rest of the world or return to Westeros, face his enemies and become the man he was meant to be when Jaime took the white: lord of Casterly Rock... or perhaps he will end up advising the winning side of the war.
I believe that Jaime will kill Cersei as I think he's the valonquar and then I would really like him to live but I feel that he's not going to survive.. Tommen and Myrcella will unfortunately die before Cersei 'cause she's to outlive all of her children.. And I also believe that Tyrion will become hand of the king and I secretly hope that Sansa will realise how great he is and give their marriage a chance :)
The Lannisters are doomed, Jaime is going to survive and go into exile, while cersei will get killed somehow, most likely by one of her closest allies, tyrion will not come back, and will become a really rich dwarf, LF will take control and RULE THE WORLD