PokerStars No-Limit Hold'em, $4 BB (6 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: FCP)

MP ($540.85)
CO ($232.40)
Button ($673.40)
Hero ($402)
BB ($201)
UTG ($496.50)

Preflop: Hero is SB with K , Q .
1 fold, MP raises to $12, CO calls $12, 1 fold, Hero calls $10, BB calls $8.

Flop: ($48) J , 4 , 2 (4 players)
Hero checks, BB checks, MP checks, CO checks.

Turn: ($48) 4 (4 players)
Hero checks, BB bets $20, MP calls $20, CO folds, Hero calls $20.

River: ($108) K (3 players)
Hero checks, BB checks, MP checks.

Final Pot: $108

I think pf call is standard, and with two overs + FD vs 2 players who aren't being too aggressive I can call $20 into a $88 pot.

The river is what concerns me. I think I should have put in some sort of value bet, but the BB is aggro and likes to take pots away from people - so I opted to check and hope for a reasonable bet to call.

Furthermore, if were to bet and either opponent raises something serious, do I call? I think I would, but I'm not sure it's a call I'd like to make.

bet or check is fine, I tend to bet here $70-$75 looks about right

and if you bet 75 into the 108 pot, would you call a pot sized raise? what about a shove? (from MP)

If you bet this needs to be a bet fold IMHO. If you can't find a fold for a raise then you need to just check.

I'm not saying to do it every time, but please mix in a squeeze here a good percentage of time, especially if MP opens frequently. Re-raised preflop, this hand plays out pretty easily.

On the turn here, I'd take a stab at it. On the river, I don't know that there's huge value in betting.

I agree. Squeezing is especially profitable if he opens for 6BBs for no reason here. Aside from preflop, which I don't really like, I think the rest of the hand is fine. I don't see any value in donking the river into 2 other people.