Is a noun a action word?

No, a noun is a Word for a person, a place, a thing.

A verb is a Word for an action.

That being said, many nouns are also verbs:

You can dock your boat at the dock.

You can paint the house with paint.

You can fish for some fish for dinner.

And a noun can be a Word for an action, a thing; the present particle of a verb can function as a noun called a gerund:

Swimming is a good activity.

Dancing can keep you fit.

You can earn a living cooking.