"nothing more than a stuck up snotty teenager!" - delightful! What do you think THAT statement makes you and your friend?
Why did they split up?
Bear in mind you are only hearing ONE side of what's gone on.
As for the "her" including quotes - are you 12?!! You're certainly not acting your claimed age of 28!
"but to take that right away from a man attending his daughters birth or even being in the waiting room" no such right exists! When it comes to a birthing mother her needs and that of the baby are all that really matter to be honest. She IS very young and even if she weren't ANY birthing mother may well not want their EX at the birth for damn good reasons! Stress can add to birth difficulties, slowing Labour and making complications & intervention more likely.
"proceeded to the hospital anyways without her say so and asked the midvives if he was allowed to see his daughter and they we're more than happy enough to oblige" with absolutely NO PROOF that he was who he claimed, did have a baby there and without checking with the mother?!!
I'd be complaining to that hospital and ward on the basis of shite security! For all they knew he was there for nefarious reasons or was abusive!
"yesterday she went and got the birth certificate without his knowledge once more, only this time she got it done WITHOUT his name on it" which is absolutely her right to do! They're not married so he doesn't have any rights on this automatically. As there's unmarried she can't put his name on the birth Cert if he isn't present anyway.
"he's been seeing that child 2-3 times per week, providing for her" which he should be, and not in order for what he gets out of the situation. I'd love to know what "providing for her" really looks like.
"and she's took everything a father should be allowed to experience in favour of her own well being." She gave birth 6 WEEKS ago! Damn straight her well being and that of the baby's is the priority! Especially when it sounds like the birth was traumatic and baby very sick afterwards. Certainly more important than your mates "poorly hurt feelings"
"Now that he's not on the certificate it means he has no parental responsibility, it means she can't demand CSA from him as he's not binded by the certificate in order to do so" WRONG! And frankly that makes me doubt your claim that he "provides" for his child! She can still claim via CMS (CSA no longer exists) and I hope she does. He doesn't need to be on the birth Cert for that to occur.
As the couple are already separated it makes far more sense practically and legally for the child to have the mothers surname. There's no "right" for a father to insist on their child having their name.
I'd say she's actually behaving very sensibly.
"Oh and she also messaged him after she told him about the certificate that the midwives influenced her not to put him on it (I deem this another lie as there's no history which would say otherwise)" actually that's entirely possible, they'll have met many other mothers who've experienced difficulties as a result of having the ex on the birth Cert and their child having ex's name.
"He's a very nice man, devoted to his daughter, loving caring and has a heart of gold" 🤔 oh yea he sounds it!
"he's never been controlling, abusive nor jealous of anything" you can't POSSIBLY know this for sure, people like that don't go around telling others they're abusive, possessive, controlling gits!
Unless you're actually talking about yourself...
Advice for your mate?
1 grow up
2 get over yourself and lose the ego!
3 pay a decent amount of cm NOT just the cms MINIMUM legally required amount and do it WITHOUT having to be chased
4 build a relationship with your dd - start by treating her mother with respect, patience and understanding NOT bitching like a tantrumming toddler when she makes decisions you don't agree with but which are in her and your daughters best interests "waaaaahhhh it's not faaaaaiiiir"
5 stop bitching to your mates about the mother of your child.
HTH