I know you can paste the Color Correction from one clip to another using Paste Attributes...but what about Balance Color? If I have an interview, do I have to run the Analyze and Fix/Balance Color for each clip? Or is there a way to paste that as well?
That wouldn't make much sense as each clip has different requirements. To be honest- I find Balance Color rarely useful because instead of making changes you can further adjust in the Color Board, it just does a best guess that you have no way to finely control.
The short answer is- no. You can just select multiple clips and Balance Color, and each shot will be balanced according to its needs. But there's no way to use that tool to make all shots consistent/balance relative to each other.
It's much better to learn the Color Board tools and work with the waveforms. Balance Color is a very basic, automated tool when you have no time/don't know how the better tools work.