Utilizing a single core to 100% doesn't show in perf mon as single cpu being fully utilized
1: The scheduler is moving the load between cores. This is a known behavior.

2: Because the processor affinity is actually a core affinity and you can not move a task away from a core if that is the only core allowed to run it.

3: Not really. Things get a lot more complex because of parallelization anyway. In general, SQL Server - unless you do very complex analysis - is a lot more memory / IO bound than CPU bound. Now, with SSD you can actually overcome this - but mostly I dont see that.

You can find that a query uses a lot of CPU - which is always something nice to optimize - but not necessarily whether it is single core bound.

If you need that, maybe an instance configured to use only one core may work. I mostly find that to be of limited use - because in large scenarios, as I said, you either are not CPU bound or with paralellism not single core bound.