Are non-degree courses a viable option to offset a low master's GPA? I am planning on applying to Ph.D. programs in the US in Computer Science and I have a bad GPA of 3.33/4 in my MS(Computer Science) degree.
Would taking non-degree courses in CS in my target school and getting really good grades, help me increase my chances of getting a Ph.D. Admit there? Also, since I am paying for those courses and taking them, would it be ok if I approach the professor and ask to work on a research project with them? Would they be able to write me a letter of recommendation in the future when I consider applying to a Ph.D. program in that same department?
This wouldn't hurt, but whether it helps depends on the admission process at that university and how competitive it is generally.
Another possible benefit is that the faculty (at least a few of them) will become familiar with your work. It also shows some seriousness of purpose.
The letter of recommendation may be possible.
But, have you explored the option of just applying. You may be making assumptions about how important your GPA is in the process. Many things are considered, including letters you might already be able to get and how strong your background is generally, and even undergraduate work.
If you can discuss your current situation with someone at the university, do so before you make decision.