If you have MSP at the time of the birth, it will be covered. However, if you go into labour early before coverage, you are out of luck. The child will also NOT be covered and if born early, will likely require a stay in the NICU. Expect a massive bill in the tens of thousands for even a short NICU stay. If longer, the bill could be a million dollars or more. If you can't afford that, don't give birth here.
There is no such thing as a "grandparent visa" and caring for a child while on a TRV is considered illegal work, so don't expect that your mother will be approved.
You may want to seriously consider deferring your studies and having the child in your country.
Parent and grandparent super visa
Information for parents and grandparents, including applications for super visas, processing times, what to expect when you arrive in Canada and how to extend your stay. It is based on their site. Go check on it. Thank you