Is it possible to buy a primary residence and live in it but also rent it on AirBnB when I'm on vacation or on weekends when I'm away? Are there a certain number of days the house must be owner occupied to stay within the mortgage guidelines for OO?

As long as you don't own another property I doubt anyone can claim you don't live there, regardless of the short-term rental stuff. For taxes the IRS usually considers anywhere you live more than 6 months your "primary" residence. 

Quicken Loans said you could only rent a primary for two weeks a year. Does anyone know if this is a requirement with all lenders or just them?

@Chris Weaver

It all depends on the lender. Some lenders don't care what you are doing with the house at all. As long as you are paying the mortgage, they couldn't care less. 

@Blake Brose is right but don't forget Insurance, and the IRS.

From what I understand if you buy a primary residence with a low down payment you often have to live in the home for a certain period of time. Is that not what others have heard?

Lookup Vacation Home occupancy, which limits the number of days you can use it and still consider it non-primary. Sure the STR would be treated similarly.