Let's say on a strat with 21 frets, will a 22 fret neck fit as well?
Yes, as long as it's the same scale length (25.5"). For a 22-fret neck, the fingerboard should have an extension which sits above the body so the actual main part of the neck is the same length as a 21-fret neck.
Are all the fender neck pockets the same size, so I mean can you just take a neck from a Tele and bolt it on a Strat and/or vice versa?
No, most Strat necks have a rounded end and most Tele necks have a square end. A Strat neck will go in a Tele OK, but it leaves gaps in the corners of the neck pocket (which can be covered with a scratchplate). To put a Tele neck on a Strat, the neck pocket will need a bit of surgery.
Which metrics of the old/new guitar parts do I need in order to do this right?
Basically, as long as you use Fender licensed parts like Warmoth, WD or Allparts it shouldn't be a problem getting necks and bodies which fit together - of course some neck pockets may be
slightly loose and some may be
slightly tight, but that's wood for you. :)