Is it normal to have arguments in your head?

I can't speak for normal but I know I do that all the time. One of the most common (false) myths about psychology is that talking to yourself means you are insane. So long as you are aware whether you are speaking to a real person or a mental projection you are fine.

I do this all the time. Levi-UR is right, it's not what I would call abnormal I'd say. I do this a lot when I'm angry or upset and have nobody to vent to. My head just argues with itself in made up scenarios so I have somewhere for my frustrations to go.

It's a bit like an internalized version of esprit de escalier. Pretty much every single person I know does this, so yeah, totally normal.

Normal is a stupid word, honestly. It is perfectly fine though to argue with yourself in your head. I do it all the time as well. It helps you sort out your thoughts, and automatically divides up the pros and cons, or the two sides of your argument. It helps you pull a conclusion.
Also, everyone thinks back on arguments and wonders what a better / smarter response would have been. You essentially help yourself process it and get over it.