Your 9. Bd4 is a blunder, allowing your knight to be captured with a discovered attack to your bishop you just moved. Opponent is up a piece then.
Please tell me why I keep making mistakes.

Your 9. Bd4 is a blunder, allowing your knight to be captured with a discovered attack to your bishop you just moved. Opponent is up a piece then.
Knight taken with check. His knight taking the other knight was the only option I see. Don't allow people to take a piece with check if you can avoid it.

You just need to get better at chess. However, you are unlikely to get better at chess by playing exclusively speed chess. You would increase your chances of getting better at chess if you were to....
Play Longer Time Controls...
For many at the beginner-novice level, speed chess tends to be primarily an exercise in moving pieces around faster than your opponent while avoiding checkmate, in hopes that his/her clock runs out sooner than yours. And/or hoping to notice and exploit your opponent’s blunders while hoping they don't notice yours. The reason for this is that in speed chess there is little time to think about what you should be doing.
It makes sense that taking more time to think about what you should be doing would promote improvement in your chess skills and results. An effective way to improve your chess is therefore to play mostly longer time controls, including "daily" chess, so you have time to think about what you should be doing.
This is not to suggest that you should necessarily play exclusively slow or daily time controls, but they should be a significant percentage of your games, at least as much, if not more so than speed games which, while they may be fun, do almost nothing to promote an understanding of how to play the game well.
Here's what IM Jeremy Silman, well-known chess book author, has to say on the topic...
https://www.chess.com/article/view/longer-time-controls-are-more-instructive
And Dan Heisman, well-known chess teacher and chess book author…
https://web.archive.org/web/20140627052239/http:/www.chesscafe.com/text/heisman16.pdf
https://www.chess.com/blog/RussBell/dan-heisman-resources
and the experience of a FIDE Master...
https://www.chess.com/forum/view/general/how-blitz-and-bullet-rotted-my-brain-don-t-let-it-rot-yours
Learn what you should be doing...
Improving Your Chess - Resources for Beginners and Beyond
https://www.chess.com/blog/RussBell/improving-your-chess-resources-for-beginners-and-beyond
https://www.chess.com/blog/RussBell

Knight taken with check. His knight taking the other knight was the only option I see. Don't allow people to take a piece with check if you can avoid it.

Like Mozart said your biggest mistake was moving the bishop to attack the knight. The reason it worked and you didn't realize it was such a big deal was because when their knight took your knight, it put you in check. Simultaneously, it opened up the bishop to attack your bishop. It was already under attack by the queen (2 attackers) and now only defended by one piece, your queen.
I actually have a process I just wrote about today that should be able to help with your middle game thought process in the future.
I can post the link if you're interested?

why did you move your rook when they attacked your bishop with a pawn? that was the most baffling move to me, as well as you deciding to sacrifice a bishop to save your queen but then you never used your queen anyway so that was pointless.

@1
"I think hard about every move I make, but for some reason I seem to make a big bad move."
++ After you have thought hard about your move and decided on a move, imagine it played and check it is not a big bad move. Only then play it.
"Please tell me why I keep making mistakes."
++ Whenever you lose a game, stop playing and thoroughly analyse it first so as to learn from your mistakes. When you learn something from every game you lose, progress is inevitable.

You should learn most important principles of a chess game. That will give you a solid understanding of a chess game and you will know what to do in every position. Then, you should optimize your calculation so you don't miss tactics in your games. Your rating will skyrocket. I can help you with all of this. Message me if you are interested.

I tried again and lost again.
Is this the limit of my progress?
I can't seem to learn from my mistakes.
It seems that no matter how much time you spend and make a move, you can only play this much.
When I was a student, I was not good at math.
Is that what's holding me back?
@12
You got a huge advantage out of the opening, but playing your knight to the rim 9 Na4?? blunders a piece. 8 Ne2 keeps your advantage.
How long did you think about 9 Na4??
How much time did you have available?
Did you consider 9 Ne2?
Why did you prefer 9 Na4?? over 9 Ne2?

@12
You got a huge advantage out of the opening, but playing your knight to the rim 9 Na4?? blunders a piece. 8 Ne2 keeps your advantage.
How long did you think about 9 Na4??
How much time did you have available?
Did you consider 9 Ne2?
Why did you prefer 9 Na4?? over 9 Ne2?
My brain just can't seem to get it, despite all the advice I get.
My efforts are in vain.

It all comes down to making less mistakes overall in games, think of it as improving your moves quality. If you aren't high elo you don't have to play the perfect game of chess, to me it was a process of simply making better moves (even if slightly). Instead of mistake, make inacurracy, small improvement in every move leads to overall better chess game and experience

@12
You got a huge advantage out of the opening, but playing your knight to the rim 9 Na4?? blunders a piece. 8 Ne2 keeps your advantage.
How long did you think about 9 Na4??
How much time did you have available?
Did you consider 9 Ne2?
Why did you prefer 9 Na4?? over 9 Ne2?
My brain just can't seem to get it, despite all the advice I get.
My efforts are in vain.
So in regards to your knight movements, check this out. It's really short and simple. It will help you a lot.
https://www.chess.com/blog/Dumbluck626/nowhere-to-run-1
And really as far as making mistakes, we've all been where you are at one point or another. Don't beat yourself up. Progress isn't linear either. It's not like you can study five, ten or even a hundred lessons and magically not make mistakes. You'll definitely improve if you do that but chess is highly complex and you'll be making mistakes in nearly every game you play for years to come.
The best advice I can give if you want rapid improvement is to find a club near you with engaging players who are willing to show you what they know.
Next, take time to study on your own. Watch youtube videos, look up articles, and read books that are suited for your skill level or slightly above.
The 100% fastest way to improve though is with a coach. Coaches are able to analyze your gameplay and quickly define the areas where you could use the most improvement and offer advice and specific resources so you can grow as fast as possible. Plus they can play games against you and discuss your thought process and theirs in real time.
I'm actually doing a drawing to give away a free coaching session in the near future.
It's free and easy to enter. The details are in the comment section of the link below.
I hope this helps!
https://www.chess.com/blog/Dumbluck626/nowhere-to-run-1
I think hard about every move I make, but for some reason I seem to make a big bad move.
What am I missing?