New father struggling with basics

A week ago today my partner gave birth to our baby boy at 36 weeks, he's very tiny and has a birth weight of just over 4lbs, he's doing incredibly well and got discharged from hospital yesterday after some additional support regarding feeding etc over the last few days, now we're home I struggled in the hospital to get him to feed (formula not breast) and now we're home it's even worse. I can barely get half a bottle fed, he just refuses and falls back asleep, I'm 6ft 3 and struggle to even pick him up as he's so tiny and I'm full of anxiety over hurting him, not doing well enough regarding feeding. I've also struggled with such small nappies and learning how to get them done so all in all I feel I'm failing him and my partner, and blame myself for the days in hospital as maybe if I'd been able to feed better he'd have gained weight quicker and therefore discharged quicker...

Everything feels doom and gloom and I just need some advice from people who've been there, hoping I'm not the only one that is...!