if parents get divorced and then wife has the children and she gets remarried, do these obligations fall on the new husband (new father) and the old father no longer has these obligations
Anonymous,
The Gemara in Kidushin (29a) says that if the biological father does not fulfill his obligation to give his son a Bris Milah, then the obligation falls on the Beis Din - no mention of the stepfather. It seems that the stepfather has no special obligation for this Mitzvah. I believe the same applies to the other obligations listed in the Beraisa there - Pidyon ha'Ben, Talmud Torah, etc. Nonetheless, whatever the stepfather does to make sure these obligations are carried out is considered very meritorious. The Gemara (Sanhedrin 99a) says that anyone that raises someone else's child is considered to have given birth to that child.
Kol Tuv,
Yonasan Sigler