Whenever I get a villager infected, if they then kill another villager, that villager dies.Yes I am in hard mode so they shouldn't be dying. The same zombie villager is unable to be put into minecarts. The first one might not be a bug, but the second one definitely is.
I cannot reproduce the killing problem. You should check that your zombie villagers are not suffocating. For example, they may be suffocating in a ceiling if they end up standing on top of the minecart. The problem of not getting in the minecart after conversion is tracked at MCPE-76831.