I created a nap routine for cot naps when DS was 6 months old (he’s now almost 1). In the nursery I change his nappy, put his sleep bag on, white noise machine, dummy, close curtains and then put him in the cot awake - I also tell him it’s nap time and tell him to have a nice nap.
i then “hide” at the bottom of the cot on the floor (!) out of the way and watch him on the monitor on my phone to see how long it takes him to get to sleep - or if he’s rolled into a corner etc and needs to be brought back down to the middle. I try to leave him alone to just work it out himself and he usually does. Sometimes if he’s rolling around a lot I’ll need to shush or pat him but not v often.
First time I did it he hated it - it took 30 mins for him to go to sleep for 25 mins. But second time it was about 15 mins and he slept for an hour - third time was 10 mins and he slept well.
the first time he was crying so I shush / pat him and he knew I was there but didn’t pick him up.
I started by doing one cot nap a day initially and then went up to two/ day so he got used to it and then all of them are in there now unless we’re out and about and then he’ll have a pram nap.
i read it was important to do a nap routine for the cot so stick to this religiously as he knows what it means.
now it usually takes a minute or two for hkm to go to sleep…..occasionally it might take 5/10 mins and if he’s overtired and I’ve missed the window then it can be up to 20….but this is unusual.
to answer your other q’s - he isn’t grumpy as he’s generally well rested and it didn’t interfere with his night sleep. I will say though that we don’t and have never co slept - he was preemie so this wasn’t an option, so he has been used to sleeping on his own since birth.
hope this helps!