Sorry I should have said “interaction with a local immigration office”.
At an airport or land border they will not care if you have filed a TM30 or not.
Any foreigner regardless of nationality should have a TM30 filed within 24 hours of arrival at their accommodation. Hotels usually do it automatically, many house owners or Airbnb hosts don’t bother.
When you return you (or your landlord) should file a TM30 within 24 hours. Many people don’t bother and unless you need interaction with immigration you don’t really need one. Some office don’t have this requirement if you’re returning to your main abode.
If you don’t stay 90 days you don’t need to report and the clock resets to day 1 on your return.
I have no experience of the Manila embassy but generally you just have to be in the country of the embassy that you’re applying at to qualify for applying. That means being in Cebu should work for you.
You’ll need a residence certificate for buying (actually to register the car in your name) the car AND for your licence. Be aware that they are only valid for 30 days (or until your existing stamp is for - which we is the sooner).
This is a classic case of why you need forums like this to tell you specifics rather than rely on Google. Google will happily tell you where the 80+ offices are located but doesn’t specify what office to use if you’re in Bangkok.