Congrats on your son and for successfully breastfeeding! I breastfed my son for 10 weeks, at which point we found out that his acid reflux was so severe that nursing him actually made it worse. Through the advise of his pediatrician and a pediatric gasteroentorolgist, I stopped breastfeeding, switched him to formula and add lots of rice cereal to each of his bottles (he is now 6 months, drinking 4 oz bottles and in each one has 3 tbls of rice cereal). Do not do this without consulting a dr first though.
On the topic of reflux, we were told not to allow Cody to sleep in the car seat, and actually, to keep him out of the car seat for at least 30 mins after feeding (which, of course, is not always feasible). The reason for this is that the carseat keeps them in a scrunched up position, which can impede the milk traveling through the digestive track. Cody spent a lot of time in the bouncy seat and in our arms. We were told to keep him semi-upright for at least 30 mins after feedings.
As for the sleeping in the crib issue, its up to you. Different things work for different people. Cody has only spent three nights in bed with us, and two were because he was sick and couldn't breathe if he wasn't elevated (the other was the night before we left for vacation because his bassinet was already packed). At 4 months old I began working on getting Cody to go to sleep on his own. I would give him his bottle, kiss him and lay him in his crib. I would stand next to him and pat his back and "shhhh" until he fell asleep. After a couple days I cut back the amount of time I would spend patting and "shhhh". About 2 weeks later I would just lay him in his bed, tell him to go night-night and walk away. Sometimes Cody would fuss (not cry) for a few minutes, and occasionally I would have to put the pacifier back in his mouth and pat his back to get him settled back down. If Cody would actually cry I would pick him up, settle him down and put him right back into his bed. The time we allowed him to fuss would start with 2 mins, then 5 mins, then 8 mins. The maximum was 10 mins. After 1 week, he was going to sleep on his own. Now all we do is put him in his bed and walk away.
We were blessed with a great sleeper. At your son's age its perfectly normal for him to need to eat every 3 hours around the clock (and breastfed babies tend to need this longer than formula fed babies). At the direction of your pediatrician you can work out cutting out middle of the night feedings usually around 4-6 months. The "rule" with Cody is that if he wakes before 5 AM, we ignore him until he starts crying (often he just goes right back to sleep). If he starts crying we give him the pacifier, pat his back and tell him its sleepy time. If its after 5 AM we give him a bottle (and he goes back to sleep until at least 6.
As for tummy time, I wouldn't stress too much about it. One thing you could try is doing tummy time on you. Lay on the bed and put your son on your chest. This will encourage him to lift his head to look at your face, which will help with building the muscles.
Sorry this turned into a novel. I hope I was able to help you some!