Can you park a kayak trailer there .?

Yes, you can, but you may need to park away from lake cause parking lot often packed.

Yes

Yes you can. David's right tho. I've gotten there and there will be tailors parked taking up 3 to 4 spots and nothing is ever said. They may direct you to a certain spot if the regular parking is full but just go, you won't be sent away and staff can direct you the best place to park. 100% fact though yes it can positively be parked there.