How exactly does having a question that I posted being closed, affect me? Does it increase the chance that I'll be banned?
As Kyle Kanos mentions in the comments, the question ban algorithm is a secret, even the diamond moderators don't know the details. But we do know that closed questions with a negative score aren't good, and that deleting such questions doesn't help.
I can only see one closed question on your profile, and it has a positive score, so you should be ok, unless you also have negative-scored questions which you've deleted.
However, in that question you state:
I know that PSE doesn't usually accept questions like this, But I'm really lost.
Knowingly posting an off-topic question is a bad idea, even when you're desperate. It could even encourage people to close-vote or downvote.
On the other hand, that question is almost on-topic. We have a strict policy regarding homework-like questions here on PSE. As the close notice says, you need to ask about the "underlying physics concepts" which will help you do the homework problem. And you've kind of done that! But your question is dominated by that photo from the textbook(?), and that photo makes your question look like a typical off-topic homework question.
My advice is to get rid of that photo and write any equations you want to refer to using MathJax. Clearly state the relevant concepts that you're sure about, and then ask about the thing that's puzzling you. Eg, "I know A, B, and C are true. And I think that D is also true, but that would imply Z, which doesn't seem right". Remember to focus on the concepts, not the arithmetic.
If you edit your question to make it on-topic, it will go into the review queue, and it will be bumped to the top of the Active page, so there's a reasonable chance of it being re-opened (although that's not guaranteed).