Being a (first?) newborn's parent is full of stress and anxieties. I had delivered about a hundred babies and cared for even more than that by the time I had my first, and was confident that I would know enough about babies not to be stressed. I advised new mothers on a regular basis, after all. Ha! At about the two week mark, I broke down uncontrollably into tears, completely overwhelmed. I say all this because feeling inadequate as a new parent and developing complexes is pretty much the norm. It doesn't go away very quickly, so expect to live with it for a while.
As @swbarmes2 stated above, not maintaining their position on the (percentile) growth curve is the benchmark for worry. Your baby has frequent doctor/caregiver appointments right now, so make the most of them. Write all your concerns down and don't be afraid to take the time to get answers from the caregiver. Between visits, call the office's nurse for questions that need answers which can't wait.
Waking the baby to eat has it's pros and cons; make sure your doctor has recommended feeding every 2-3 hour around the clock before you try to keep this schedule. It's possible that you're getting enough into the infant while they are awake to get by. Take advantage of the times your baby is awake to feed (cluster feeding). Ten feedings in 24 hours averages out to a feeding every 2.4 hours.
If feedings are necessary every 2-3 hours, then you do need more tricks up your sleeve which will make life a bit uncomfortable for your baby to keep them awake. You've tried some of the common recommendations. Here are a few more.
Undress the baby down to the diaper before feeding; if the room is cold, use a light blanket. If they're nice and warm, they'll stay sleepy.
Feed skin-to-skin. This also means baby is undressed and so is the person doing the feeding. This is actually very good for the baby's well-being, and not too bad for the parent, either.
Use a cool, wet washcloth and stroke the baby's face/head/uncovered feet/whatever.
Bright-enough lights will be somewhat disruptive to the baby's sleep, too.
Switch breasts as soon as the baby stops sucking/starts to fall asleep.
Burp the baby sitting up supported on your thigh, not over the shoulder. Don't be afraid to jiggle the baby gently.
Try breast compression to keep milk flowing if the baby stops swallowing.
...it's difficult to get him burped enough that he doesn't spit up later in the night.
If the baby burps when burped, they are "burped enough". Babies spitting up is common in infancy. Also, you might just have a "spitter"; they really do exist. All of my clothing had stains on the shoulders from my first's constant spitting up, which didn't stop until about nine months of age. If it's worrisome, talk to your health care provider about the possibility of reflux.
This is a trying time, no doubt about it. But if the baby is gaining weight appropriately, they are feeding well enough.