Service amperage is given at 240V. In other words, if each leg is breakered @ 50A, then the service would be considered 50A.
If the main breaker were a single-lever double-pole unit, then the rating on that lever would be the service rating.
Probably not. The meter pan must be rated for the amperage, as must the panel. Also, the service entrance conductors need to be rated for the service (that is the customer-owned wiring from the power company (POCO) hookup through to the main breaker).
Finally, the POCO would have to allow for the service in question -- they might need to upgrade their conductors, the service drop. (At a house with overhead service, that would usually be the lines from the utility pole to the house).
So it's possible that the service entrance conductors, the POCO lines, the panel, and the meter socket could be rated to carry, lets say, 100A even if your main breaker is only 50A. It's unlikely though.
POCOs do frequently install service drops that they rate for a higher ampacity than the service, if the service is under 200A. So that might be the one piece that does not need upgrading, but the POCO would have to make that determination.