Jothar: You would take a small bite of the dairy so as not to have a Bracha Levatala and then you do not eat more. (I believe Rav Schachter quotes that from R’ Akiva Eiger but if it’s within the first hour you can’t eat it. He quotes from the Zohar that within one hour is a real Issur D’Rabannan but after that is just a minhag and the Minhag can’t force you to make a Bracha Levatala.)
Yes, you can throw the hot pizza out.
No, The Issur of Bishul Basar B’chalav only applies to Basar Beheima Tehora Bechalav. There is a Machlokes Haposkim about Neveilah Utreifa. But Beheima Temei’ah everyone agrees is Muttar to cook Bechalav and Muttar Behana’ah. (There is also no Issur of Basar Bechalav if you would eat it but it’s obviously Assur because you ate pork.)