Is there a way on an iPhone to record what's happening on your screen? Like a screen shot but video instead of just a pic?

Gen 7

Yes. You've been able to do that for almost a year now with iOS 11.
Instructions from Apple

Yes it's possible it's called screen recorder and it should be on your phone. You can record whatever is happening on your screen with it.

If by Gen 7 you mean an iPhone 7 (which isn't the 7th generation for the record) then yes. If you are on the latest iOS there's a screen recorder built in. Access it (after enabling it) through Control Centre.