It's possible he sustained some sort of cellular damage from the cold exposure at birth(if it was cold at the time), possibly damage to his heart, and this is affecting his growth and overall health.
There are two instances I saw an undersized kit successsfully treated and it caught up in size and health to it's siblings. First was a baby rabbit I got that was at least half of the size of her siblings, was a bit skinny, and had a pot belly. A change of diet when I got her, to a high quality pellet and free fed hay, somehow corrected whatever was wrong. The pot belly went away and she actually grew to be bigger than most of her siblings. I can't say for sure, but I suspect it was the poor quality feed she was on before coming to me, that was causing her problems, and/or she may have possibly had hepatic coccidiosis.
The other time was someone I know had one kit that was undersized, half the size of it's siblings. Just not thriving. The owner decided to give the bunny a 10 day course of fenbendazole for deworming, and it worked. Afterwards the fkit started doing better and gaining more weight, so that he eventually started catching up in size to his siblings. So in this case(and possibly mine) it was an intestinal parasite load causing the failure to thrive.
So parasites are a possible cause. Maybe you could have a fecal test done to check for that. But if it's a genetic cause, or possible cell damage from hypothermia, then I'm not sure what can be done. Unless maybe having the heart checked by a specialist, or having a blood test done to check liver and kidney function. But I think the kit is so small still, that it might be difficult to do much testing until it's bigger.
With the eyes, you may need more of a lubricating eye ointment, that stays on and protects the eye better than eye drops, especially if the cornea is being rubbed by fur, eyelashes, or the eyelid. If there's infection present(sticky white discharge, white clouding of the cornea), I would expect to see some improvement by 5 days, so you may need a different antibiotic than what's in those eye drops. You may also need your vet to get a closer look at the eyelids to see if surgery might be needed to fix whatever defect is going on with the eyes and causing the ongoing rubbing and irritation. Otherwise they eyes could possibly sustain permanent damage to them.
https://www.vetlexicon.com/treat/lapis/freeform/eyelid-entropion