I used to know a formula for determining P. I. T. I. (principal, interest, taxes, insurance) payments being $(interest rate x 100) for every $1000 of home value. Does this still apply as the best way to figure mortgage payment and what is a good formula to determine rent in relation to this?
1) That isn't a formula; it's an approximation given a bunch of assumptions about "typical" mortgage and taxes and insurance costs. It's good as an initial guess for deciding whether you might be able to afford a house, but if you want something for serious budget calculations you need to actually calculate mortgage costs for the specific loan and find out what insurance and taxes on this particular house are likely to run, and obtain the actual cost per month from those. And then add your best estimate for what maintenance costs on the property are likely to be, which depends on the particular house and location.
2) After you know the real cost of owning this house per month, and the additional costs of managing a rental (including the fact that the rental unit is likely to spend a few months empty), you can determine what income rental needs to produce in order to cover its own cost. Then decide how much profit it needs to produce to make the whole thing worth your effort; that's going to involve comparing it with other ways of investing your money, which may produce different results if you're going to occupy part of the building. Only you can decide how much profit it needs to produce to make it worthwhile, since only you know your own risk tolerances. You also need to decide how much of the accumulating equity in the house should be counted in this equation, and what you believe the future value of the house will be.
If you can't answer all those questions in detail, you aren't ready to make an offer on the property.