If a user of a shared folder deletes files that I uploaded to Dropbox, does it free up my space?

Yes it would - because it would also delete the file from your account

Thanks!
And what happens if another person of other team upload new files to the same folder. Does it take up space on my account?
I mean, I uploaded files to a shared folder of another team. I need to free up space. If I delete them, and then they upload them again. Does it take up space for me again? Makes sense?

Hi Nachi_81, welcome to our Community! 

Think of a shared folder like a common "basket" between accounts. You have the same basket in your account, as everyone else. 

Therefore, the "apples" that someone adds there -aka the files- take up space in your account too. Any of these changes sync between Dropbox accounts when it comes down to shared folders. 

I hope this helps!