The mobile version is just a remote way to access the VM on a computer with Parallels installed, so this computer (a Mac) has to be on and connected to the internet.
Windows is not running on the iPad, it's running on the computer, the iPad has to have an internet connection to access it.
So...
1 - Yes, a computer with Parallels Desktop for Mac and an active internet connection has to be running.
2 - Yes
3 - Only when you have an active internet connection on the iPad.
4 - Yes it is, the key point is the upload speed of the internet connection of the computer hosting the Windows VM.
5 - Parallels creates a Virtual Machine that runs Windows, so everything that can run on windows should run well (except programs that specifically detect they are running in a VM and don't allow it, very rare thou).
Last edited: Oct 12, 2011