A. Yes, you can transfer or rollover your previous HSA account to a new institution, such as a bank or a brokerage house.
For example, Wells Fargo' HSA account charges no monthly fee and you can trade a wide range of mutual funds.
You can also open a self-directed HSA account at TD Ameritrade, then fund it through your previous HSA money. In this way, you can even trade stocks.
Transfer means your previous HSA provider sends you a check and the new HSA provider, and Rollover means your previous HSA provider sends you a check, and you deposit it at your new HSA provider.
Unfortunately a HSA account is individually owned, you cannot combine two different people's HSA accounts into one, unless one of the two dies.