Can I damage my phone by doing android programming on it? I am a beginner to android programming and I want to use my personal phone that I use daily to test my programs, but I am not sure if that is a good idea.

Is it possible to somehow corrupt my phone by trying out my programs on it?  In what ways might this be possible?

The phone is unrooted; would it be possible in a rooted phone?
No, you can't. As you surmise, if you root your phone and write programs that use root to change system files or settings that you can't normally change, then you can break the phone that way. The risk is not really any different to running root programs that other people have written.
If you don't root the phone, or don't use root in the apps you're writing, then you can only do what any other app might do. You might run the battery down extra quickly, or (if your app has the appropriate permissions) delete pictures, contacts, &amp;c., but debugging your own app won't cause any kind of system corruption or random problems.