I can't say if they actually do check or not, but I can say they are supposed to.
As I said before, an arrest is not a conviction. For a conviction you would need to be formally charged, found to be guilty and actually received sentence. Whatever that sentence may be. Even a suspended sentence is a conviction for immigration purposes. After all the main purpose is good character.
Yeah, the mayor of Davao is quite famous. That's why it's one of the safest cities in Philippines.
May I suugest you visit for a few weeks before going down the SRRV route.
Life in the Philippines may not be all you think, and may also be much more expensive than you think.
Look before you leap