Does using an app send my IP address and device identification info to the app maker?
This completely depends on the app. There's nothing that by default sends identifying in formation about your system to the App developers, the App would have to have been written in order to have this behavior. Depending on the app, however, it's possible that some might.

You didn't mention if you're on iOS or Mac OS. If you're on Mac OS, and you're concerned, or curious, you should consider installing an outgoing firewall like Little Snitch. What this will do is show an alert message asking for permission every time any app tries to send data to the Internet. You can use the Little Snitch network monitor to identify what data is being sent, to determine if your privacy is being violated. You can also prevent the app from sending data at all.

If you wanted to do the same for iOS you could use software on your router, but this is an advanced topic and beyond the scope of this answer.