Preflop:

Your $10 raise pre-flop seems a bit small. I'd make it around $16. On the otherhand, AQo on a 9 handed deepstacked table is not even that great. What do you do against a 3-bet? You could have also limped along. Raising a bit more polarized is probably better in this spot, with for example AK and some lower suited aces. This way it is more obvious what you should do against 3-bets.

Flop:

On this flop, four ways, I would strongly advice against c-betting with your hand. I think your particular holding must be one of your worst combinations to c-bet, since you don't have a flush draw, straight draw or even a backdoor flush draw. Your bet is unlikely to get through all 3 players. If you get raised you have to fold. Other than an off-suit ace or queen, which are only 4 cards, no turn card is really good for you. And even if you hit one of those card you are, especially when hitting the queen, you cannot be so sure you are ahead. You should check and give up on this hand.

Turn:

You hit the perfect card. Keep in mind, this happens 4.5% of the time. At this point I think you should keep firing. I agree with you, you are likely ahead at this point. However $50 is too small. You are giving your opponent 3:1, which means that he only need 25% equity to continue. Given that you also have $40 behind he is also getting some implied odds. You are giving him the right price with any good draw. Since you have less than pot behind. Shoving here is not crazy. If you had made it $30 on the flop, shoving here would be more comfortable. It is important to plan ahead.

River:

With so much in the pot and so little behind it is getting a bit silly. I do think you should be good here most of the time. Villain can have missed flush draws, missed staight draws, a weaker ace, or maybe a hand like KQ. I guess you should bet and get the last $40 from your opponent. I don't think he is folding any decent holding and I doubt he is bluffing with his missed draws, since you are unlikely to fold.

Preflop:

Your $10 raise pre-flop seems a bit small. I'd make it around $16. On the otherhand, AQo on a 9 handed deepstacked table is not even that great. What do you do against a 3-bet? You could have also limped along. Raising a bit more polarized is probably better in this spot, with for example AK and some lower suited aces. This way it is more obvious what you should do against 3-bets.

Flop:

On this flop, four ways, I would strongly advice against c-betting with your hand. I think your particular holding must be one of your worst combinations to c-bet, since you don't have a flush draw, straight draw or even a backdoor flush draw. Your bet is unlikely to get through all 3 players. If you get raised you have to fold. Other than an off-suit ace or queen, which are only 4 cards, no turn card is really good for you. And even if you hit one of those cards you, especially when hitting the queen, cannot be so sure you are ahead. You should check and give up on this hand.

Turn:

You hit the perfect card. Keep in mind, this happens 4.5% of the time. At this point I think you should keep firing. I agree with you, you are likely ahead at this point. However $50 is too small. You are giving your opponent 3:1, which means that he only need 25% equity to continue. Given that you also have $40 behind he is also getting some implied odds. You are giving him the right price with any good draw. Since you have less than pot behind, shoving here is not crazy. If you had made it $30 on the flop, shoving here would be more comfortable. It is important to plan ahead.

River:

With so much in the pot and so little behind it is getting a bit silly. I do think you should be good here most of the time. Villain can have missed flush draws, missed staight draws, a weaker ace, or maybe a hand like KQ. I guess you should bet and get the last $40 from your opponent. I don't think he is folding any decent holding and I doubt he is bluffing with his missed draws, since you are unlikely to fold.