I've been overwhelmed by requests for several weeks now, so I want to go on vacation hold. I'd still be able to reply to PMs (yay for auto-reminders), but I barely have funds left. However, I'm worried that using "Vacation Hold" may affect my current transactions, like books that are still being mailed and also what I've/will be requested.

Books you have mailed will not be affected. You'll still get your credits when it is marked received. Any wishlist books you have on Auto-Request will be automatically sent to you without you having to do anything other than mark received when you get it. You will continue to move up the queue for any WL books you don't have on Auto-Request.

Your books on  your bookshelf will not be able to requested by anyone however your books will still continue to move up the queue so that your books will be closer to being requested.

Assuming you have enough credits, you can still request books with your shelf on "vacation hold". VH does not affect current transactions including books to be mailed.  They still have to be mailed even though you put your shelf on hold after the books were requested.

I've been overwhelmed by requests for several weeks now

I note you joined PBS on 1st May. I can understand that 12 book requests in 13 days could make you feel overwhelmed. It may help to know, it is not unusual  for new members to feel this way initially, as many of the first books they first post may be wishlisted or in short supply here, so they are quickly requested. This normally settles down, and then requests are much slower, as your more heavily posted books take some time to move up the FIFO queue.

Other solutions that may help you, as well as vacation hold, is putting books on your reminder list, which will let you know how many copies are in the system, or, at the least, putting them on your TBR list before posting, which will let you know if they are wishlisted. These can somewhat help you control how many requests you receive.

And, welcome to PBS :-)

Thank you for helping! I'll keep in mind about everything! Especially Reminder and Wish lists. I didn't think to use them like that before.