Hi Maya, welcome to the forum. There's a wealth of information here, and many knowledgeable people here to help you.
Oh you don't have TO many! I have 7 myself.

Many here have more than that.
Yes, closing your cc's WILL hurt your scores because of reduced utilization. But your payment history remains for 10 years(I think that's right).
If your FICO scores are high enough, you can apply for different cc's, that carry no AF or monthly fees, to replace those cards WITH AF's. But get the new cards BEFORE you close the older ones!

I'm in the process of doing just that. One at a time, just to be safe.
BTW, what are your FICO scores like?
My scores range from 638 to 655. I applied and was approved for 3 bank cards. None had AF's or monthly fees. Just to give you an example.