In the first hand, it's not crystal clear what happened pre? You isolated against three limpers with a $20 raise and only the small blind called in the end? Anyway, given that there apparently isn't much left behind on the turn as played, you probably could have just got all the money in on the flop. Still doesn't seem like you did anything wrong; the guy put his money in way behind and sucked out on you. You definitely want to play more pots with that player lol.
Second hand, I'm still very confused about the action, but you got the money in way ahead, yet again. You want to be up against A3o in that spot. The fact that in this particular instance you got coolered doesn't matter. It feels like you're looking at these situations wrong if you want "A3o out of the hand". A3o is awesome to see. What you don't want to see is AK, AQ, A8 or 88. It's still possible that you misplayed the hand (I can't really say because, as stated, I don't really understand who was in the pot or who did what lol), but it seems like you did fine.
Check-raising with 77 on 883...in general that seems a little ambitious, but I think calling off the re-raise is the biggest problem here. As you said, you're often just completely crushed in this spot when you get called.
The reoccurring issue with your thought process is this desire to "get players off a hand". And that is part of poker, yes, you like to deny players their equity. You are pretty happy if someone with AK folds when you have 77 on 883, because they don't get to realize their equity and you get to win the pot right away. However, folding out worse hands is, typically speaking, not as good a result as getting value from worse hands. You'd rather people put in money when behind, allowing you to win a bigger pot. That's what "getting value" is all about. Think about it, when you have AA, do you just shove all in preflop to discourage people from calling because you're terrified of being outdrawn? No, you put out a smaller raise because you don't want everyone to fold. You want at least someone to call and to put money in postflop when they are most likely behind. Incidentally, this is exactly what happened in the first hand, and in that hand, you won a ton of EV. You lost a bunch of money, but you made a good series of decisions with a high positive expected value. And that's all you can control in poker.
When you're playing live, you're not playing a lot of hands in a lot of time, and it can take a long, long, long time for playing better than your opponents to actually be rewarded. It would help if you put some time into studying the game to better understand how these situations you're describing are actually really good for you in the long-run, regardless of the results of the individual hands.
To start with, let's compare the fates of AJo and A3o on a board of AA8. AJo wins about 70% of the time, loses about 10% of the time, and there is a tie about 20% of the time. You can easily find a program to calculate this sort of stuff just by googling. In this exact instance, you can win, lose or tie, but if you got in this spot say a million times, you would have millions upon millions of profit, almost surely. Now, you don't get this exact spot a million times, sure, but you get very similar ones, and if you keep getting it in good, and play enough hands, you will win money.
Of course, I'm not saying just keep doing what you're doing and you'll win, because maybe there are other issues in your game (well, I already identified calling off with 77 on a board of 883 to be not too great). I'm just saying that, from what I can tell, it seems like these two hands were played very profitably.