S.C.
It's very very normal for your 5 week old to sleep all the time. It's what babies do :) They eat, sleep, and poop! :D You won't have to worry about teething for a VERY long time yet! The best thing to do is to take it as it comes. My first daughter never once bit my nipple. My second, however, was a biter. OUCH! I would break her latch with my finger, sit her up, look in her eyes and say "NO! NO BITE!" then I'd let her nurse some more. If she did it again, I would do the same thing, but then I'd put her down. Honestly, it was still a little hit and miss, but she bit much less after I did that a few times. Each child is different. You may never ever have and issue with biting. You just won't know until you get there!
If you want to pump, I would recommend keeping and eye on your milk supply. Do you still have a lot of milk in your breasts after nursing? Do you have a time of day when you're most full? I was always really full of milk in the mornings, so that's when I did my pumping. I was a SAHM, so I didn't have much need for a HUGE amount of stored milk, but it was nice to have some on hand. You can pump whenever it's convenient for you. Your body will respond to the pumping and begin to make more milk. Our bodies work on supply and demand. The more the baby nurses (or you pump) the more milk you will produce.
There are some "experts" that will tell you that your baby should nurse for 30 minutes each time he nurses, 15 minutes on each side. My daughters were more fond of snacking. They would nurse for about 15 on one side, take a break and want to nurse again after about 30 mins. You can only feed him for as long as he wants.
Babies will sleep through the night when they're ready, at least that's how I feel. I'm not a fan of sleep training or the CIO method. My oldest is 13.5 months and she just started sleeping through the night. We co-slept so it wasn't a big deal. I highly recommend co-sleeping to all nursing mothers. You don't actually have to get up to feed him, just roll over! :) That said, if you are or decide to consider co-sleeping, make sure you are doing so safely!
Congratulations on making the decision to give your little man the absolute BEST start in life!