virtualbox.org

If a virus or some sort or malware infects the host, how likely is it to also infect the vritual machine running Windows? In particular, will a keylogger or trojan from the host be able to pick up keys pressed or do any damage to the VM?

There is always a chance. The real question is, are you willing to risk it? This subject has been going around here for quite some time, search a bit and you will find your other answers.