Can I download 3rd party songs on the iPad and add them to iTunes Match? I wonder if i can buy and download songs e.g. via Bandcamp in Safari, and then add them to my iTunes match right on my iPad?

I know how to do that with iTunes on the Mac, but it would be neat to have this also on the iPad.
Nope. You won't be able to add the in iTunes and thus you won't be able to add them to iTunes match.