Most frustrating/worst “stalemate/draw in the history of Chess.com!

I recommend you start playing real people. Sounds like you've played the bots enough to give you an idea of the game. Anyone can give up a stalemate. I saw it in a grandmaster game several weeks ago. As you learn , you will become wary in certain situations. You will learn to avoid it.

Well, you know about the stalemates, so you just need to look out for them.
When you do your move, think about what his counter-move will be, in this instance where he offered his queen, you need to think, what will his next move be after I take the queen? And you can see he would have no possibility of a move, so therefor you can't take it.
I pretty much always try to go for stalemates if I'm in a losing position, it's up to the opponent to see through my attempts.

You should totally play real people more often! You'll get the real thrill and tension of actual gameplay. It also teaches you the time value of chess because computer games aren't timed. And, computers may be extremely consistent, but — and this sounds weird — computers "aren't good at being bad." Their mistakes are very calculated and not the types of blunders you'd see from humans. Practicing with computers is still beneficial; but don't practice entirely with computers.
You shouldn't be embarrassed to lose, even to a child. You progress more when you lose than when you don't participate at all. And humiliation sure does force people to remember things, doesn't it?
And as for your stalemates, I had the same frustrations when I picked chess back up about a month ago. I developed the habit of ALWAYS considering whether or not the opponent's king (or at least one other piece) can move after I make my next move.

To prevent stalemates, simple check:
1) do I check my opponent's king?
if no:
2) do I have hella lot of pieces on the board? (this increases chances of stalemate)
if yes:
check to make sure enemy king has somewhere to move.
The safest way to avoid stalemate is to check your opponent every move.

There are lots of children on this site at all levels.

Click "Play" and pick a time control.

my language isn't English, but that should be enough. Chess.com will always pair you with opponents of similar rating.