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?