Hi there, well done on getting the interview! In answer to your questions:

1) The term you are looking for is "PEG" - Private Equity Group, or PEG Ringfence. In Bain, this is separate to the rest of consulting, called the General Practice, "GP".

It basically refers to work we mostly carry out for large private equity funds in either performing the Due Diligence on a potential asset (i.e. company they are considering to buy) or doing the post-acquisition value creation (i.e. after a company is bought, increasing its profits). Note it's separate from Bain Capital or actual Private Equity (i.e. we only advise, don't actually invest).

2) Your question is a bit unclear but for market sizing, the most important part is laying out a clear and logical structure upfront. An issue tree is a useful tool to use here. Once you've done that, assumptions are less important, and depending on the case you should feel free to discuss your assumptions with the interviewer. Also, be ready to evaluate your method after and think of potential simplifications, and what assumptions you would want to test more.

Good luck!