Is there any way to transfer VirtualBox VMs, with their operating system and all their files intact, to another computer?
Cloning a VirtualBox VM explains the cloning process on a Windows 7 64bit host cloning an Oracle Linux 5 64bit guest using Virtual Box 4.0, which I believe matches your situation more closely.
You can also take a look a the following articles for reference:
I'm not sure to understand what you're asking... If you're talking about the app, there isn't a workaround, you must reinstall it. Regarding the VMs, you can simply copy them to a the other computer, look for the directory where they're stored (Look in File->Preferences to find the Default VM Folder).
Yes, what Host OS are you running? Did you store all the files and VMs in their default locations? If it's Linux it is easy to switch to another Linux, but moving from/to Windows is a bit involved.
Note that you must shut down all the virtual machines, not just sleep them or save their state. You must actually shut them down.
Open Virtual Box, highlight the machine you want to copy, click machine on the menu, click show in explorer , copy the entire VM folder to an outside drive, transfer the folder to the new machine, open virtual box and click machine , add machine , go to where you transferred the machine to. and open sesame