Will 2017 Home and Business CD/download version recognize my 2016 return done on Premier CD/download so I don’t have to re-enter rental fixed asset history?

Yes, it should import just fine. But still check it as soon as the import is done.

Yes, 2017 Home & Business will recognize the 2016 Premier return and transfer the information from it (assuming, of course, that you have the .tax2016 file on the computer you are using for 2017). All TurboTax editions use the same file format.

I don't see an option on the menu of 2017 H&B that allows 'Transfer from prior year' or similar

Click Start New Return and read the screen. Prior year import can only be done when starting a new return. It is not possible at any other time.