bsolutely agree with PP. While all of the other things may vary from being 'unlikey to be significant' through to 'minor, small issue'. Feeding to sleep is your big issue.
Resolve the feeding to sleep "problem" (it need not be a problem) and you will solve the main bulk of all sleep issues.
The Science
Humans sleep in cycles as an evolutionary left-over from caveman days when we could be eaten by predictors when sleeping.
In cycles through the night, we have light sleeping phases. In an adult, you may barely notice these. It's the times you shuffle positions, unconsciously glance at the clock, shuffle around and go back to sleep.
You are just checking you are safe, without overly disrupting your sleep. If you went to sleep in your bed and during one of these light sleeping phases realised you were in a car, what would you do? You wouldn't roll over and go back to sleep. You'd freak out, be wide awake very quickly thinking WTF?!
Same with baby. Goes to sleep in your arms, with part of mum in her mouth, listening to your heatbeat. Wakes up alone, in dark, no mum for comfort. Freaks out, no settling back to sleep.
Going to sleep in the place she will stay asleep is important.
Your baby has the added confusion that sometimes in the brief wake up you are there cosleeping. But sometimes you aren't.
Cosleeping
One way to solve this is to simply embrace cosleeping full time, all the time.
Baby falls asleep next to you, knows he will always wakes up next to you and can breastfeed at any time.
That may involve moving around your routine. Maybe baby stays up with you until you go to bed. Maybe you go to bed earlier and consider your bed as "me time".
Independant Sleeping - without crying
Maybe you don't want to cosleep? That's fine too.
You said: I've tried so many times to put him in the cot drowsy.... That won't work. From being breastfed to sleep, if you want to do with without loads of crying and distress, the jump is too great there.
From breast feeding to sleep, your first aim wants to be fed until drowsy (not asleep) then cuddle to sleep. Then into cot.
Next step is feeding before bedtime, cuddle to sleep. Into cot asleep. (At that point congratulate yourself that you arent feeding to sleep)
Then cuddle to very drowsy, lie next to cot and comfort by leaning into cot for last bit. And so on.
Independant Sleeping - with crying
The whole gradual withdrawal process as described above can be done much quicker. Less gradual. This will give faster changes but will come with distress.
Or controlled crying. Or cry it out.