In Bridge you can, it will display the thumbnail for the first page as far as I recall
Only if you save it with previews of all pages. Not a good idea.
In InDesign you can have page previews in the pages panel but given that we have no real idea of what the OP is after, it’s hard to answer.
Not a good idea.
Why not? I have my preference set to all pages and never have problems.
I’ve found it needlessly blows up the file size, but to each his/her own.