The CPU will operate at the max FSB capable of the motherboard as long as the CPU can handle that FSB. CPUs can also run at lower FSB than rated. This is called "underclocking" the processor.
TRUE to the first question, FALSE to the second.
Other factors limit the speed of the CPU such as RAM speed. A lot of motherboards set the RAM and CPU to the same FSB, so the limiting factor here would be the slowest capable product. Some motherboards let you set separate FSBs for both, getting past this problem, but generally, RAM likes to run at the same FSB as the CPU.
The only thing that limits whether a CPU will work in a motherboard is if the CPU is designed for the socket on the motherboard.