Matt immediately starts to ram Jessica when he pegs her as Peter's biological mother. It's a lot of anger... but it's rooted in his own abandonment issues — Maggie abandoned her infant son and never bothered to come back for him. But Maggie had the excuse of postpartum depression, while Jessica's only trauma was due to external causes. So Matt briefly thought the mother of his son threw the boy away just because she didn't care. Explains his reaction perfectly.
The Punisher is surprisingly amenable to help protect Peter, even agreeing to do his best to avoid killing in front of the boy. That's not only because Frank doesn't want to see another kid hurt as long as he can prevent it, his relationship with Daredevil also plays a role. Even if he accuses the Devil from Suicidal Pacifism, Castle grudgingly respects him, and certainly doesn't hate him to the point he would wish for Matt to live through the same nightmare than him: outliving his baby.
Peter's brilliance in sciences is actually In the Blood — in canon, Alisa Jones boasted she had the ability to study high-level maths, and her intelligence is noted. Peter takes after his maternal grandmother.
All the Defenders are happy to learn about Peter, but Danny's enthusiasm looks a bit too much. Only, it's not about lacking maturity, it's about the fact he was raised by monks — not adoptive parents, but monks as a community. Asian societies put extreme emphasis on the importance of community and groups, and small communities often share responsabilities between their members. As such, Danny's eagerness to become part of Peter's life comes from the fact he considers raising the boy as a duty for the Defenders as a whole, not just Matt and Jess.
Kilgrave sneeringly asking about the father of Jessica's unborn child and his obvious satisfaction when he learns it was only a tryst. Twisted and possessive as he was, Kilgrave would have forced Jessica to push Matthew away if Matthew had still been around, and this is the less horrible option - it would have been likelier for the guy to order Jessica to kill Matthew, just because he wanted her for himself.
Between Jack's probable generalized anxiety disorder, Maggie being hit hard by postpartum depression and Matt's crippling insecurity, the Murdock bloodline certainly looks like it suffers from mental illness. Now, seven-year-old Peter is already having self-worth issues... Let's hoping he would accept therapy.
How, exactly, did HYDRA learn about Peter being a natural-born enhanced? And what do they want to do with him?
