I get the feeling from reading this whole thread that you don't actually have this deep, burning hunger to travel. You've said a few times you feel pressured by your dad to travel, like he has this expectation of you to travel. You've said a few times that you feel almost obligated to travel because you have this opportunity to do it cheaply through your mom. But I didn't really see anything stand out that said *I want to travel so badly it keeps me up at night.* I didn't see excitement there.
I also didn't really pick up a *travel to teach english* hunger either. Again, you mentioned an *obligation* to get something out of the whole homeless experience with the teaching english courses. It seems more like duty, again.
The only place you expressed a genuine interest in traveling to was Melbourne where, clearly, you would not need to teach english. Why Melbourne? Because you could embrace painting there.
You want to paint. That is very clear. You seem to be putting all these obstacles in your way and misdirecting yourself in the most fantastically complex and convoluted ways in order to avoid a life of painting.
Are you afraid to just really let yourself go and just paint your life? You don't have to go to Melbourne to do it. You don't have to move out or get a *home base* or travel or any of that. You could turn away from your computer and do it right now.