How could dosage be regulated if vax was put in food? Children and very large people would get the same dose. The idea is stupid so I have no doubt the derps have at least considered it.
That depends on whether cooking denatures (permanently changes the shape of )the spike protein or the mRNA.
Poisons do their work at a molecular level by screwing up the body’s internal chemical processes. In particular the spike protein binds to ACE2 receptors while in the virus; the mRNA within the lipid microcapsules gets pulled into cells and then gets to work telling the body to make spike protein.
If either of them gets their shape changed enough by cooking (heat = molecules wriggle around more == change their shape and can’t change back when they cool off), in general, all bets are off.