Hi, welcome. absolutely happy to hold your hand as you unravel some things and get on track for your little fellow to sleep better!
First off, don't beat yourself up. You've done fine, followed your instincts, decided something needs to change, found some information and asked for support. That is brilliant. As my husband said when I felt terrible "You've done your job. Baby is alive - you're fed, cleaned, etc. as needed."
Also know that your baby has some of these skills already - you witnessed him resettle himself - you know he *can* do it. Once his routine is better for him, he will likely do this/not need to.
Lots of these issues you have will resolve partially or fully by just getting the daytime naps sorted, so lets do that first, then we can tweak/train whatever is left. Making these changes will take some effort - he will likely cry because you're changing things he's known all his life so you have to be ready to stick to it before you start, for his sake and yours. I'd suggest tackling things in this order:
1. Get routine sorted - A times, naps and feeds at reasonable times
2. Getting sleep in crib
3. Night wakings / whatever else is an issue.
FWIW, what I did with my son at 5 months was 2.5hr A times by the clock for a few days (for you, this may be as much as a week just to make sure you're well and truly through the regression that usually happens around 5 days before you start trying to get him into the crib). So you'd be doing this with your props (except feeding to sleep) to get him to sleep and keep him asleep. We'll wean those off eventually but whilst his body is getting used to sleeping proper naps, you can keep some things the same or its too hard with a spirited and things go south very quickly.
I'd suggest a routine like this (shift to line up with your ideal WU/BT, whichever is more important to you):
7 - WU, feed
9:30 - nap
11 - wake, feed
1:30 - nap
3 - wake, feed
5 - nap
5:30 - wake, feed
7:30 - asleep in bed for the night
https://kellymom.com/bf/pumpingmoms/pumping/milkcalc/Have a read of this and just make sure you're feeding enough at each feeding/enough through the day. If he's not taking large enough volumes, you can give him a main feed when he wakes from naps, then top up 45-60min after that so he's getting slightly longer between feeds and you can gradually shrink that gap between main feed and topup so he's taking feeds further apart if you so desire. Alternately, you can just keep them and know you'll replace the topups gradually with solids in a month or so. I know what I'd choose with dealing with bottles, but that's totally up to you and what you're comfortable with. Two night feeds at this stage is absolutely normal, so don't worry too much about that.
Its quite likely you'll read what I've written as think 2.5hr is too much, he could never do that, etc. He's got plenty of signs of being chronically OT with those short naps and I get that he will be cranky and look tired at 1.5hr - he's used to that and he's doing it from habit now. That long happy waking at 4:15am - classic sign that he needs more A time. I've just gone for a round figure that is average for this age and we can tweak from there but give it a few days to settle in.
Any other questions, ask