Do I have to use iMessages or can I use a regular messaging app

An iMessage is a type of message that is sent, not a messaging app.

The messaging app in an iPhone is called simply Messages, no I.

Messages (no i) can send iMessages and regular SMS messages to non Apple devices.

Why exactly don't you want to use the Messages app?

Elizamettler wrote:

messages+

You mean Verizon's Message+? https://www.vzmessages.com/introduction/index.html

You can use it sure if your carrier is Verizon. Don't know if you can use it with other carriers. You would need to ask Verizon that,

Not sure what that has to do with FaceTime. FaceTime is a video and audio call app. Again, you don't have to use it if you don't want to.

What exactly is your issue? We cannot help you if you don't explain and provide full details.

What is a "regular" messaging app?

Then just stop using it and don't accept FaceTime calls. But that has nothing to do with messages. Is Messages + a 3rd party app from the App Store? If it is you can use it if you wish.