Can anyone take M.Phil (regular) and MA (open university) parallelly?

It would not be possible to take admission in M.Phil without completing your MA as for M.Phil you must complete the post graduation of the desired field such as MA, M.Sc, etc.

Yes, you can. Graduation is the min eligibility criteria for getting admission to the PG course. But don't get confused in both the course and be careful that both the exams don't clash on the same date. All the best!