1) Yes — to some extent all new dads feel this
2) dunno only you can tell
The mum spends 9 months coming to terms with it whilst a father only has the stark realisation its actually happening when the baby pops out and theres not refund and return policy. Hey you knew it was coming but no one gave us the handbook.
Dont be fooled into thinking one size fits all, every kid is different and each parent has to deal with their own kids 24/7 ( see above posts re relentless) . After all, who else is there at feeding times and 3am when they wont sleep! ( I dont see any of those armchair know it all parents giving a hand!).
We all find our own way with our kids and they will build a relationship with you with the time you spend with them whether its alot or a little.
What I will say is dont cave into the other peoples way to bring up your child, eg do it like this and do it like that. Or take the short cut and say its easier if someone else to do it. You learn via your own experience and hence will be rewarded for it accordingly even if it involves a few wrong turns along the way. Dont let other people judge you or make you feel inferior because of it!
Dont worry too much as I reckon most dads feel like a spare part in the early weeks. Bear in mind its also a learning adventure for the mum to so why not agree to do it together. Ask questions , enjoy the tough times cos they pass all too quickly even though it doesn’t seem like it at the time. Good luck and enjoy!