I can give you answers based on what we do here at Skywest which is pretty much the was everyone does it.
How is the flying time shared between Cap.and F/O?
We try to keep it equal. Split up the legs as even as possible. One captain I flew with would do all the outstation flights and I would fly into the hubs, then the next trip we would swap. I like doing it by round-trips better.
What is the ratio[hrs flown by Cap./ hrs flown by F/O?
Pretty equal. See above!
Who decides?
Depends on the captain. I'm pretty laid back so I'll give my FO the opportunity to fly his favorite legs, etc. I usually do the very first flight of the trip- to set the tone, sort of.
When F/O is flying who is PIC , if there is an accident who is responsible ?
No matter who has his/her hands on the controls, the captain is always the PIC and holds sole responsibility for the flight.
How is the flying time loged?
The captain always logs PIC and the FO SIC no matter who is actually flying the airplane for that leg.