Thinking of camping July 10th-12 single with tent, do you think if I show up you will have a site for me?

Pretty sure you could best bet call for available space just to be on the safe side so you can at least have a plan B.

Available first come, first serve sites go on sale each morning at 8am

Possibly

Probably yes because you have the daily sites

Maybe. I'd put it at around 60% based on my past experiences. Tent sites are weird in terms of availability especially when they're first come, first served. It really ends up boiling down to how attentive the park staff is.

They might check their website