(a) Why are Beth Din not told to redeem the first born as with the Brith Milah? If it is because of monetary question between the father and the Cohen , the Beth Din also gets involve in monetary matter.
(b) The Agadata on the bowing of Rav Acha where the serpent heads were cut every time he bowed down in the Tefilla of Marriev. Why Acha bowed seven times, if he only had to bow four times in the Tefillah , even if you include Alinu Leshabiah it will not account for the seven bowing that he did to eliminate the serpent.
The Gemarah says that he was alone in the Beth Hamidrash , so we have to assume that perhaps there are more than four bowing in the Tefillah ?
Shabtai Nacson, Toronto, Canada
(a) The Halachah that Beis Din takes over for the father (in the case of Bris Milah) is learned from a special Pasuk, Himol Lachem in the plural. There is no such Pasuk for Pidyon.
Logically, we can easily justify why the reason the Torah does not tell them to get involved in Pidyon. First, if people would know that Beis Din would pay the Kohen the large sum of the Pidyon (and thereby fulfill the Mitzvah of the Torah) if they do not pay the Kohen, they would all leave it for Beis Din rather than pay from their own pockets! Second, if a Bechor is left "unPaduy," he is not personally affected by that fact. He simply has not fulfilled a monetary obligation. However, it would certainly affect him on a religious level if a Jew were left uncircumcised because his father did not circumcise him.
Of course, Beis Din can force the father to pay from his own money for the Pidyon (even by confiscating his money, or whipping him, etc.), just like they can enforce any Mitzvas Aseh that a person refuses to fulfill.
(b) Your question is asked by the SHITAH LO NODAH L'MI. He first points out that there is no mention of him bowing in Ma'ariv; Rashi says that he was praying a special Tefilah uttered to kill the beast.
In addition, he suggests two other answers. Either he only bowed four times and decapitated four of the heads. Once most of the seven were off, the beast died. Alternatively, the last three bows were performed while he was stepping back at the end of Shemoneh Esreh and bowing while facing left, right and then forward, as we do when stepping backwards the three steps.