Can we bring spare shoes into the park?

I recommend bringing a small backpack, you can place the backpack aside when you get on rides. Don't forget to bring some water.

you could take whatever you want in the park you just can't take food and beverage they make you pour that out when you go through the metal detectors

Yes you can. I was recently at Hurricane harbor and took my daughters water shoes in with no problem at all.

Yes, but they will check your bag when you go in there.