Why does my guinea pig bite me? And how can I train him to pee and poo in the...

First, try to make the rest of the cage a non-poop zone. That is, for example, one corner is the food dish, one corner is the water bottle, and one corner is the bed, so the little guy automatically chooses the remaining, neutral corner as the toilet. You can also try cleaning the rest of the cage very thoroughly to make sure he doesn't smell some old pee or something in a place where you don't want him to be thinking about the potty (but don't use harsh cleaning products or anything scented!). Then place some soiled bedding or poop in the place you want him to go potty, and if you spot some soiled bedding somewhere else in the cage, remove it promptly to reinforce the idea that only one spot in the cage is the toilet.
Also wash your hands before handling your pet. He may smell something tasty or threatening, and that is why he is biting your fingers. My pigs don't do it, but my hamster used to always get confused when I wore nail polish, and he would nibble at my nails; so try to identify things like that. If your pet is just nibbling, he might just be playing; if he is really biting at you, he might be scared for some reason, so make sure you are supporting him well (hand under back feet/rump and hand around ribs/belly) when you hold him. It is actually quite rare to have a cavy who will give a good bite!