I’m sure Caroline will come back to you with the details of the boat company she uses for Nice/Monaco transfer.
There are lots of restaurants and bars for you to enjoy over the weekend where you don’t need tickets, there are also parties, clubs and yacht parties etc. which you would need tickets for.
The atmosphere around the harbour, along the start/finish straight and throughout Monaco is great so if it were me I would stick around that area. Casino Square will be good also but on Casino Sq itself you really only have the casino, Cafe de Paris and the American Bar of Hotel de Paris (latter two are expensive).
La Rascasse is good on a Friday but as I’ve mentioned in previous posts the atmosphere is somehow different, more aggressive, on Sunday after the race. This is from personal experience and feedback from quite a few of our guests. There are lots of venues in the harbour and along start/finish straight so don’t worry about finding somewhere.
In Nice there are lots of tourist trap restaurants and bars but there are many good one also, Tripadvisor should keep you right and if you PM me your email address I’ll send you the info pack and restaurant suggestions we send our guests.
Don’t hold me to this but from memory I think the last train back from Monaco was just before midnight in 2012.
I hope that helps, do let us know where you decide to watch the race from and why, it is always helpful for others.
If I can help with anything further or you just want to pick my brains let me know.