Primary residence conundrum

[Colleen West]

I have a really bizarre issue. I have been under contract on a new construction house for about 8 months in Austin, Texas. The house is set to close on May 14th, and everything has been finalized with my rate locked in with the lender. I was approved under my current W-2 income which is around $100,000. However, I recently decided to take an internship offer with another company which will be a significant pay cut. This offer doesn't start under June 7, so I will technically hold on to the same income and job I was approved with until about a week after closing after which I would put in my two weeks notice. 

Under these circumstances, are you obligated to notify your lender that you know your income will be changing shortly after closing? Additionally, while this home is supposed to be my primary residence, I'm undecided if it would be affordable after the income cut and would need to consider renting it for a period of time. This is a bizarre situation where this "internship/payment" is only 12 weeks, after which they'd convert me to an FTE back around the same income I was before (pending program goes well).

 In this case, if I put tenants in for 3 or 6 months while I'm doing this internship, is this allowed and still called my primary residence if I intend to occupy it as soon as possible? Or would I need to notify the lender as well I might not be able to move in right away? While I'm definitely not trying to commit mortgage fraud, I love the property and want to close on it - and there'd just be a lot of unknowns right around that time.