$2/$5 blinds, 9-handed, $500 effective.

Reg raises to $20 UTG
Fish calls $20 in MP
Hero calls $15 in BB with A4hh

Flop ($55) is As 8h 6c
Hero checks, Reg bets $30, Fish calls $30, Hero calls $30

Turn ($135) is 3d
Checks around

River ($135) is 7s
Hero checks, Reg bets $45, Fish folds, Hero calls $45

Is this standard play?

Its not horrible but I wouldn't call it standard. I would fold preflop probably 1/2 the time depending on the players. When I call and flop an ace I'm stuck in this exact situation too many times. The river line is player dependent.

I'd need to know a lot more about Reg to decide, but generally I'm OK with calling in each of the spots here.

Reg's range should be very strong to open UTG. PPs and big aces pretty much always. Pretty much all of that rage will c-bet. The big aces will often bet turn, but not always, because the board is so dry. Basically his entire range is WA/WB here. If I were reg with a big ace, I'd usually bet anyway to try to get max value out of Fish's weak aces.

So we get to the river and everyone checks, basically his whole range is betting here. While you would expect his bluffs to be at least half-pot, it could be a post-oak. You only need to be good 20% of the time, and that's quite reasonable here.

With no reads, this is an easy fold pf. Once the "fish" calls the flop bet, you should be out. I guess I call on the river because it is cheap and to teach myself to stop calling other players "fish" when I'm the one making bad moves.

Very easy fold pre

Anyone that disagrees has a massive leak

I'd lean towards pre being a fold rather than a call but that depends heavily on villain's preflop ranges. That being said, calling pre is never AWFUL.

Flop is a super easy call.

Without knowing more about reg, the river is a call due to pot odds.

pre - 100bb deep it's borderline. Deeper you can call pre.

Flop call is fine, top pair back door nut flush draw
turn is fine
River is meh, looks like he wants a call, but that price is really good. I can go ether way but most likely calling.

Pre is ok w fish in hand, but folding is probably better.

Flop is marginal, but folding is probably better.
River is a fold, and folding is definitely bettter. The fish is still in the hand when the reg bets riv and you overcalled flop.

Can you explain further?

Getting 3 to 1 in BB with suited A4 with fish in pot. Doesn't seem like a "massive" leak at all. Seems marginally fine here to call preflop.

It's 2/5, chances are the rake is high enough to make the hand not marginally fine. It almost assuredly sucks oop only 100 bbs deep anyway barring esp abnormal play by either villain. Also judging by OP's previous posts he likely isn't good enough to overcome theoretically marginal spots so this should be a snap fold for him