Is installing an outlet inside a cabinet with LPG tank a good idea?
Not a clue in the Phillipines, but the wire can be lengthened to whatever you want, using a same sized wire - that only needs to have electricity for ignition.
The hole for the tubing - through what? Metal will need a grommet, wood needs just a hole, and the space for the bottle needs a bottom vent at least. I guess the regulator is on the bottle, so that could go outside, with a longer pipe through the wall (again, protected) if it's not going to be potentially stolen.