Can you use your own kayak on the lake or do you have to rent their paddle boats?

Yes, you can but they charge a fee.

I guess I actually answered my own question. We were there and asked the employees. They said they charge a $5 fee to use your own boat, but you can do it.

Any entry fee is there to enter the lake Fairfax park?

not sure they have them already there

I don't live in Fairfax but it's low-key outrageous that they charge you to put your own boat in public water. Public facilities should be run for optimal usage, not profit maximization.

If you camp at the campground you might be able to sneak one in

You have to pay for the boats