Not talking to anyone about this in real life is foolish!
You BOTH need help, support and advice in real life to address this.
This is exactly what parents and health visitors etc are for. I'd been a nanny and was phoning my grans and mum for advice on colic and teething etc as much for the reassurance I wasn't doing something completely stupid as anything else, plus with sleep deprivation I wasn't on the ball and "forgot" stuff I bloody well knew!
Had he much experience with babies BEFORE becoming a father?
My ex had none! He'd never even held a baby until we had dd, there's a photo of him holding her for the 1st time and he honestly looks like someone has handed him a grenade with the pin pulled out! 
And she wasn't even awake at this point she was snoozing away!
The only way ANY parent learns to settle a baby is practice!
You didn't know what worked for her straight away did you? You persevered, tried different things... and then you happened on what worked for you and baby.
He needs to do the same.
Sometimes too what works for mum to settle baby doesn't work for dad or granny and they have to learn their own ways to settle them.
Has he done any parenting classes? He may well benefit from doing so - as much for confidence building as anything else! Would also be good for him to learn about baby development and how things are for mums postnatally so he knows what's going on. Eg so he knows about cluster feeding or sleep regression etc
My ex felt daft when he did things like put a babygro on backwards but you just laugh it off and he takes it off and puts it on properly and it becomes an amusing family anecdote.
Hell when I was in very early stages I did some daft/weird stuff too! And I was a nanny before having her - sleep deprivation really is a bugger!
LET him make (non harmful) mistakes without making it a big deal, share the things you struggled with.
My ex took the stance of "jumping in at the deep end" spent lots of time with dd, learned her quirks and preferences, developed his own relationship with her.
Eg one of his "things" was he used her as part of his morning exercise ritual - sort of used her as a free weight. She LOVED it and when she was old enough she'd be smiling and laughing at this point in her day.
He was also often the one to bathe her. We can now embarrass her (she's 21 now) with the story of how daddy got her all clean in the bath then as he lifted her to hand to me to be wrapped in a towel she pooped right down his (rather hairy!) chest! 
So then he had to have a shower while I cleaned her in the sink!
He was the only one could settle her while she had colic. She had a very particular way she'd lie on him and sleep but he couldn't as he had to be sat bolt upright for the position to work! He did that for ages then around 5am she'd settle in our bed for a couple hours and he'd get 2 hours Kip in the spare room and then go to work knackered!
The reading is great but if he can find a dads parenting class even better as then there's the group support/camaraderie element too and he can share his "mistakes" with others who've done similar in a more lighthearted way.
I bf too but ex would when it was night wakings fetch me a drink/cardi/whatever if I wanted/needed then after she'd fed if needed he'd do the burp/nappy change while I sorted myself out (she was a messy awkward feeder) so we shared the load
Don't be so quick to jump in and "fix" things if he's having trouble settling baby or changing nappy or whatever, don't hover - I know it's hard!
My ex did actually have to tell me to relax and back off a bit in early stages as I just naturally went straight into doing everything because I knew how and I could do it quicker/easier
He was like "I'll never learn if I don't get the practice in. Let me be"
Regarding how he is about her crying - he needs to understand that's just what babies do! There's not always something that wants fixing sometimes they're just "having a grumble"
My exes approach to this was to talk to her a lot! Loudly but not shouting (he was army they seem to know how to do this very effectively admittedly!) or he'd even sing to her (this was very amusing as he knew NO nursery rhymes so he'd be singing rock songs and tv theme tunes to her )
Singing calms him as well as baby btw there's a scientific basis to this, and lower toned voices are especially soothing to babies
Getting outdoors is an excellent suggestion. Lots of walks in the pram, then when she is older kicking a ball about or playing catch or hanging at the park
Re lack of parenting classes - he could start his own dads group - he won't be the only one feeling like this.
Earplugs - the squishy silicon ones are best in my experience, white noise may also help re the tinnitus
I'm another saying pnd does NOT apply to men - they may experience depression/anxiety but they don't have the hormones and physical recovery to deal with too. It's NOT the same
@Karenina40 an article written entirely from a male perspective!
er no!
It's called expressing milk, something I did 30 + years ago. I'm sure it's still a thing.
Not everyone can! I couldn't