Can a virus from a VirtualBox VM affect the host computer?

Very good question.

The main reason a virus could propagate from VM to host Operating System is via the network. Once you start using bridged networking between the host and guest things get more risky. Your machine and the VM are seen as 2 nodes on the same subnet. A worm which sees these 2 nodes has the possibility of propagation if such a vulnerability is found.

Yes, if you have shared folders...

Either shared folders through the VM, or standard networking.

I am not sure, and have not seen any viruses in quite a while that spread like this and edit files over a network, but it is possible.

Just because it is a VM does not mean it is safe, you just have to treat it like another physical machine on your network.

So, if you have anti virus on your host machine (and others on your network) you are as safe as you are going to be, but again... treat any VM like any other physical machine.

The only safe way to run a VM is to disable networking features (or VLAN separate it completely from your network... and not have any sort of management interface on that VLAN.) and all the host/guest integration that involve sharing files.

Unless there's a security flaw in Virtualbox that allows you to break out of the VM (and you've not patched), then no. However, it's worth remembering that if there's any network connection between the two, there's the possibility of it moving to the host, as it would move between normal machines on the same network.

Edit: In terms of checking for connections, the simplest way is to nmap the host from the guest. Use the -PN switch, incase your host blocks ping. If there is any response, then you've got a connection there. Even if you don't, there's still the possibility of a connection through another machine, if that one is connected to both the host and the guest.

technically, the answer is yes and with virtualization growing increasingly popular, expect more attacks on hosts through the guest OS in the forseeable future.