Hi B. -
First of all, you aren't doing ANYTHING wrong! I will say what everyone always tells me...every baby is different! Sure, your son is capable of sleeping through the night (not eating throughout the night would not harm him - as long as he is healthy, over 12# and your pedi has not told you otherwise), but that doesn't mean that it is unusual for him to wake for night feedings. Many breastfed babies do.
As far as solids are concerned, he doesn't necessarily need them at this age. As long as he nurses well, he gets all the BEST nutrition from that. If he is refusing the food, I would keep offering, but when he starts spitting it out (even if it is after a few bites) I would be done and try at another time. I have read it can take babies up to 15 tries before they accept a particular food. Nutritionally though, I wouldn't worry if he won't take it. It can be frustrating, but some babies are more sensitive to taste/texture than others.
If you are wanting to wean from the night feedings, I would start gradually. I would keep whichever feeding he does best at (1 or 4) and start weaning at the other time(s). If he usually eats for 10 minutes, cut it shorter by 1 minute every night, until the feeding is phased out. Also, you can try pushing the time you go to him. For example, if he fusses at 1, try not to go to him until 1:15 and keep increasing the time. I was not able/willing to let my son cry it out, so how you approach the weaning is completely up to you. I would definitely try to wean from the feedings where you know he is pacifying. That will be hard, i am sure. Try rocking or cuddling until he is calm and put him back in his crib or next to you. It may take a few tries, but after some time, he will get it. It will most likely make your nights worse initially, but in the long run it will mean more sleep for Mommy!!!
Good luck.