Probably best to go with something in the 3.5" line, unless you’re going enterprise 2.5" (which are entirely different birds than consumer drives)
Whatever you get for your NAS, make sure it’s CMR and not SMR. SMR drives do not perform well in NAS arrays.
Many years ago I for some low cost 2.5" Barracuda for my servers only to find out years after I bought them that they were SMR and that may have been a contributing factor to them not being as fast as I expected.
TLDR: Read the datasheet
Not on a flash based motherboard (so basically almost everything recent). On modern systems usually the only thing the battery powers is the clock, which is why they have a separate reset to defaults header/button/switch.
(The CMOS memory of old is replaced with flash memory, al la SD Card or flash drive)