I just got a Certificate of Residence (CM immigration office near the airport). I needed a copy of the TM 30 receipt. No lease, house book, or landlord appearance necessary.
Depends how long your license has been expired. I believe that if it's over a year, you have to start over again and yes, you'll have to do the tests. Otherwise, the colorblindness test is all you need to do at the Land Transportation Office.
The length of your initial license isn't based on the type of visa so I doubt you can change/renew to a longer one until 3 or 6 months before expiration. Hopefully, for your sake, someone will prove me wrong.