Pet food on Pesach must definitely be free of Chametz. However, Basar Bechalav is not so clear. It is a Machlokes Acharonim between the Chasam Sofer (Assur) and the Noda Biyhuda (Muttar in the Dagul Mervava) as to whether Basar Neveilah Bechalav is Muttar Behana’ah. I personally do not understand how this argument exists since the Ramabam explicitly states (Peirush Hamishnayos Kereisos Perek 3) that it is Muttar. You should consult your rav as in some cases it me be permitted to have pet food with meat and milk in it.
There is no real Heter for spaying/neutering a pet as the P’sak is brought down that the Issur of Sirus applies to non-Jews as well and giving a non-Jew a pet to spay/neuter would be Lifnei Iver.