Can I extend my 60-day visa for another 30 days at Patong immigration and what documents do I need?

There were reports that Phuket Immigration is also checking the TM 30 House registration. I would take it with you, just to be sure. It has nothing to do with being here as tourist or other wise, every foreigner needs to be registered within 24 hrs after arrival at the address. This can be done by landlord, house owner, house master or manager of hotel.

As a "tourist" you should just need your passport, 1 photo, and 1900 baht for 30-day extension. And completed TM7 form.