Should I TM Stone Edge off of my Tyranitar so it has mono-type dark moves?

Yes you'll have a 50/50 to roll fire blast. That's just how TM's roll.

That said, a bite/stone edge ttar is about as useful as a bite/fire blast ttar: it's useless. You want crunch on that TTar for sure BUT you might have a mon which needs the TM even more. Check if you don't have a higher priority. If you don't, then TM that ttar.

It comes down to whether TMs or Ttar candy are easier for you to get. There are a few niche uses for Iron tail/Stone edge Ttar if you don't want to risk multiple rerolls.
Ttar is definitely a better specialist than generalist.

On a similar note, should I put a second charge move on my smackdown (crunch & stone) or my bite (crunch & stone) for PvP?

A lot of folks advocate wait till you need it. When the lake trio show up in raids, you'll want that Darktar. Same if you have the chance to face Deoxys. If you only have one TM to invest, that Fire Blast will haunt you in your sleep.