Can an IPhone work without service?

My mom got an iPhone 6 a while ago and I was handed down her iPhone 5s. It functions Great, but it doesn't have any data plan(no service). I want to sign out of her old Apple ID so I can A new one. But I don't know what's going to happen if I do that. So what IIm really asking is:
1. If I sign out, Will I still be able to use as a normal iPhone? When I create my new Apple ID will I still be able to download games and apps and stuff?

Yes, and Yes