Should I feed my BP outside his viv?
Seems to be a split between inside and in a seperate container. There's a myth out there that feeding a snake in their enclosure will cause them to be aggressive to anyone coming into the cage. If you removed the snake from the cage and then fed, you could make an equally convincing arguement that the snake would then go into feeding mode each and every time you removed it from the cage to handle it. So to answer your question: it doesn't matter...whatever works for you. Many balls are shy feeders and eat better when they are on "their turf."

I use aspen as substrate and heard this may be harmful if ingested so Im worried about just laying a mouse on the vivs floor.
No problem if they injest a piece or two. They've got a nice strong simple digestive system that takes care of all that.

My BP is captive bred and 2 months old. Hes been feeding fine whilst at the breeder and seems very tame. How long should I leave him to settle into his new home before attempting handling and feeding him, Ive had him 2 days now and left him alone so far.
Its "standard procedure" around here to leave them alone completely w/o any handling for a week to allow them to settle in an become acclimated to their surroundings. In my experience, I've had bps that needed a week and other that needed only minutes and ate right away. Wait a week with no handling to be on the safe side.

I think that covers it!