What can you do after your queen is captured or not?

or offer draw to me or opponent and accept it...? ^^^^^^^^^^^^

Sometimes, resigning isn't the best option. Continue to play the game by trying to defend and counterattack. I lost my queen in an offline tournament and I still won by laddermate.

It's hard for me to understand what was in your mind while hanging the queen in these two games. Was that mouseslip or you thought that you checkmated the king? Because that two pawns were clearly defended, the defending pieces weren't even far away from the pawns

The OP did not lose their queen in those games, their opponents did. I think they are asking what to do in such situations from an etiquette perspective.

If you are asking what to do when your opponent blunders away their queen, you are under no obligation to agree to their draw offer. Just play on.

Was it yamenc who offered you a draw, and you accepted it? I would not have accepted their offer. Similarly, you should not feel compelled to offer them one.

Upon losing the queen with no material and/or positional advantage, it is normal for opponents to resign, like Zoro12345678776 did. However, as another post mentions, if you end up losing your own queen, consider playing on because 100 Elo opponents will likely blunder multiple times in a game.

first of all dont blunder the queen in the stupidest way possible if the queen trapped take the most valuable peice possible or make the most valuable peice trade itself with the queen also find counterplay checkmate attacks threats keep your king safe all that stuff also why did you give away your queen even though you would lose 8 points material instead of one point

The OP did not blunder their queen in the posted games, their opponents did.

Well, now I know that your opponents were blundering, not you, with that in mind, just accept your win, advance in rating, and get more serious and more challenging opponents when you get to higher ratings