Is the word store a noun?

Yes. It can also be a verb too!

It depends on the usage.

Store is a noun when it refers to the place where items can be purchased (Ex.: I bought some Apples at the store.), when it refers to a quantity that has been saved (Ex.: The library has a store of books.), or when it refers to the place a quantity is kept (Ex.: The castle has a weapon store in case of attack.).

Store is a verb when it refers to the act of saving something for later use (Ex. I will store my homework in a folder until tomorrow.).