My senior and I started pair programming to improve my code quality. He likes it and I find it fun (and convenient that he helps me) but it feels like I'm making him do my work. I also fear that I am too horrible to be trusted with code alone but if that was the case they would kick me out right?

Sounds like they invest in you. It sounds like a win to me. The most expensive cost one can invest is time.

Sounds like you are suffering from impostor syndrome.

I agree with @shdw if your senior invests time in you, he sees something in you. Don't be scared and just do the stuff, you are going to be fine ;)

And are you sure that he actually does the work for you? My junior thinks that all the time, but I only am asking questions and don't say to him what he has to do.

That's freaking awesome he's doing that. I'd take that as a compliment.

If you're that worried, sit down and explain that you appreciate working next to him but are concerned you're not pulling your weight because of it (or something like that, I'm awkward with wording).

Otherwise, dude sees potential in you abs you should keep going!

One sentence: Watch and learn.

Learn how others would solve the same problem. And this is most of the time not a one direction function, even a senior can learn from a junior!