Implied odds and a river bet

I'm still trying to fully understand implued odds, but I think this situation illustrates them. Please correct me if I'm wrong.

No Limit Holdem Ring game
Blinds: $0.15/$0.25
9 players
Converter

Stack sizes:
UTG: $18.85
UTG+1: $16.75
MP1: $4.84
Hero: $24.75
MP3: $8.18
CO: $15.71
Button: $28.09
SB: $33.05
BB: $51.68

Pre-flop: (9 players) Hero is MP2 with 6:diamond: 5:diamond:
2 folds, MP1 calls, Hero calls, MP3 folds, CO calls, Button raises to $1, 3 folds, Hero calls, CO calls.

Flop: 4:spade: 7:heart: A:club: ($3.65, 3 players)
Hero checks, CO checks, Button bets $1.5, Hero calls, CO folds.

Turn: 6:heart: ($6.65, 2 players)
Hero checks, Button bets $3, Hero calls.

I'm getting 3:1 pott odds, but the implied odds make this call correct since if I hit my OESD I can likely get $6 more out of my opponent (5:1 implied odds for a 4.8:1 draw). Am I right?

River: 3:heart: ($12.65, 2 players)

Do you value bet 1/2-3/4 pot here or push? I don't want to risk giving a free showdown in case the villain is extra cautious and the flush possibility or 4 to the straight makes him shut down. It's early in the session, I haven't seen much of the villain to have a read. I put villain on AA or AK/AQ/AJ, much smaller chance of KK/QQ/JJ. Looks like a nice opportunity to double my stack (or get stacked if he has Ah-K/J/Q/h).

Im not a huge fan of limping SCs in MP, if I play them I do so in LP and often for a raise, but almost never call a raise with them. I think you are definitely getting implied odds to hit your straight on the flop, that turn though hurts because 2 outs to a straight complete a flush, i wouldnt hate a turn fold. That river completes your straight, but complestes a flush even if he doesnt have the flush, a bet from you on a flush board will be scary and he could easily fold], if you dont bet here then you didnt get your implied odds and lose money [in the long run] and if you do bet and villain pushes, what are you going to do? As played I think you have to value bet that river for about 1/2 pot, but Im not really sure. I dont like being put into situations like this so I often avoid counting on implied odds when some of my outs may not be clean and could end up costing me more.

Implied odds refers to the money you'll make once you make your hand. So, at the flop when you think, "I have to call a bet of $1.5, to win a $6.65 pot", you're thinking about pot odds. When you take a look at your opponents stack and think, "If I hit my straight, I might get a decent chunk of that", you're thinking about implied odds.

You checked the river. If your opponent checks too, you didn't make any extra money for hitting your hand, so in hindsight, your implied odds were 0. If you bet and he folds, again, 0. I doubt he has the flush here, but if he does, and you bet, the extra money that he wins is reverse-implied odds.

If I were the villian, looking at that board, I'd be happy to check behind if I don't have the straight or flush, so I'd recommend you bet at the river. But that last card being a heart does make things difficult.