Villain is 39/19/3.6 28% aggr over 260 hands.

Grabbed by Holdem Manager
PL Omaha $0.10(BB) Replayer
SB ($6.01)
BB ($6.90)
Hero ($12.15)
CO ($7.37)
BTN ($18.74)

Dealt to Hero J K A T

Hero raises to $0.30, fold, BTN calls $0.30, SB calls $0.25, BB calls $0.20

FLOP ($1.20) 5 A 2

SB checks, BB checks, Hero checks, BTN bets $0.90, SB folds, BB folds, Hero calls $0.90

TURN ($3) 5 A 2 J

Hero checks, BTN bets $2.25, Hero calls $2.25

RIVER ($7.50) 5 A 2 J 9

Hero checks, BTN bets $5.62

I realize my flop play is questionable but I don't know if b/f or c/f is preferred. Is there ever a reason to c/c the flop in this spot with any hand?

bet flop

as played bet turn

as played call river

Don't c/c TP on that board OOP in a MW pot.
Bet yourself or c/f.

Coming from NL when considering whether to bet I ask myself does a better hand fold, or does a worse hand call? In this spot, my answer to both questions are generally no, but I thought he could bluff worse when I check. Do these same concepts for justifying a bet on dry boards apply to PLO?

If we bet flop what's the plan on an unimproved turn?

If we bet flop and bet the J turn what's the plan on a blank river?

Equity is less "locked in" in PLO then it is in NL. In NL, you could c/c KK on a flop of Axx, and if you bet OTF and get called, they probably have an Ace. In this case its different - giving a free card is a disaster - there are so many hands that will improve to junk 2pair that are willing to float a street. If you bet with the clear intention of folding to a raise, you're protecting your hand from weak 1 pair hands that will fold, or whatever other crazy stuff is out there. Strong hands will probably raise you, and weak hands may call you - and you can go from there.

If you bet flop and get called, barrel most turns.

Betting through with the Js, I may bet small on the river. You want to get crying calls from weaker 2p hands. Maybe c/c if you are facing an aggressive player, but its safer to bet. If they have 43 and jam you, nice hand.