I don't even think about a kind of routine from my kids until at least 3m, if not 4m. Until then I just roll with it.
I had the same problem with my girl, I was running everything by the clock and she was never sleeping. So I started just going by her cues and we get several decent naps and proper feeds now
This is my second time around, and I'm trying not to get too caught up in schedules and times. While I consider the times, I think it's more important to look at their cues. My bub is almost 10 weeks, so I feel you. Unless she is on me or my partner, she will generally only go down for a power nap in her bed.
What have you done to resettle him? My 12 week old will sometimes wake but I give her her dummy and pat her bottom a little and she goes back to sleep. With my first I had trouble until a sleep trainer told me to do the feed, nappy change and play in the wake period. Once it’s getting close to their wake period finishing, put them in their bassinet/cot while they are content and they should fall asleep in there and would have a better sleep. That worked for my firstborn before the 4 month regression. Regarding schedules it depends on your baby’s growth. If bub is gaining weight well feeding doesn’t need to be every 3-4 hours. I always went by cues. However my girls never let it go longer than 3 hours in the daytime. I hope that was helpful.
Just roll with it. Don't worry about when he's "due" for a feed. The 3-4hr "rule" is crap. Babies don't read the books or follow the rules. It sucks when they aren't settled because you get nothing done and have no downtime, but he's a newborn. When he appears slightly full for a bit, pass him to someone else for a cuddle if he won't sleep in his bassinet/ cot. So you might get one slightly extended sleep from him. Cluster feeding is normal and can be because of hunger, to increase your supply or simply comfort. Just feed away, try to juggle feeding and walking occasionally with one hand if you can so you can attempt to do stuff. Otherwise just get used to a lot of sitting and feeding. My little dude is 11w, and sometimes I don't put him down for long either. Generally, he's on me for most of the time from midday to about 8/9pm. But he's sleeping well at night, so I'm not going to complain.