Is there a designated area where one can keep there belongings while skating?

Single use lockers are available. You purchase a token from the entrance gate and can store your belongings safely inside until you're ready to leave. I must emphasize that is single use. If you open the locker you will need to purchase another token to lock it again

There are lockers and cubby spaces under the benches near where skates can be put on.

Yes snack bar but it's a one time use only so you have to make sure you know what you want to store while using it