rent to buy ?

Don't do a rent to buy!  There are many reasons.  What if the seller doesn't pay the taxes or mortgage?  What if the seller can't convey marketable title?  It's a bad idea since you don't get the title until after you have paid in full.  You would be better off with a lease with the option to purchase.

Rent to buy is 99% of the time a terrible idea. If you do consider this - get a VERY clear contract. You may find if you miss a single payment the entire deal is void. 

Mostly no unless it's a high paying part time job, it was thought up because the average full time wage often isn't enough to buy a house.

It is possible, but renting to own is a scam.

The fact that you are part time is on one level immaterial. It will be your income that is looked at.

So, if what you earn part-time if enough, then you will be fine

What's your monthly salary?  You still have to qualify.  Do you earn $80,000 a year working just part-time?