How fast does pork fat spoil? I have a mini-oven with a tray I use to fry my bacon for breakfast.

Quite a bit of fat leaks out from the bacon onto the tray. It sits there, in room temperature for a day or two, then I put more bacon in and fry it again. Eventually I'll collect the fat for other use or even just wash it out, but that's definitely not something I do every day.

How long can I go safely without washing the tray, just letting more fat collect, before I risk it goes bad, and need to get rid of it?

Would switching the oven on every day, whether I use it or not, just to heat the fat, to kill developing germs make this time longer?
This is an unwise practice.  While pure fat is actually fairly stable, you don't know how much residual water and other components remain in your rendered fat.  You should collect it and refrigerate it (it should last at least a week, probably much longer in practice) in an sealed and air tight container (to minimize rancidity) if you intend to reuse it.

Otherwise, you should discard it immediately.

For the cannonical answer and reasoning, see:  How do I know if food left at room temperature is still safe to eat?