Oh my dear. Hugs. Can he make it through to 11.15? If so, I would stick with the set naps. At some point he will HAVE to sleep, and if you stick with the set naps, in theory he should have to lengthen his nights. And whenever he does nap, make sure you get a rest yourself if you can
I know what you mean about the AP - I had no buggy or car either, and once LO is too heavy to carry there's not a lot you can do. It's hard.
Calpol (paracetamol) did nothing for my LO when she was teething - have you tried ibuprofen?
He's 10 th percentile and hasn't put on any weight in 3 months.
Has he always been in the lower percentiles? My LO has always been small, even now at 2 she can fit into some of her 9-12 month clothes, but she's active and healthy so that's just her. She will go for months without putting on any weight as well, then put on a couple of kgs in a growth spurt.