Yes it can.
You have to have a jailbroken ipad and the app installous
There are many. The iPad must be 'jailbroken'. Jailbroken iPads are vulnerable to exploits, viruses and poorly written apps that can affect the iPad's stability or performance. Doing this may also affect your Apple warranty.
No. Updating the iPad's firmware will remove any jailbreak that has been installed.
It depends which iPad you have. The First Generation iPad can be Jailbroken using redsn0w (search on google) and the 2nd/3rd Generation iPads can be Jailbroken using Absinthe 2.0 (also search on google for download links, you need a pc for both methods)
Yes, you can bring a jailbroken iPod, iPhone, iPad, etc. into the Apple store and get it checked out. They 99% will give you a new product.
if jailbroken you can make the ipad detect a blue-tooth mouse changing a few settings... jailbraking = void guarantee
By "jailbreaking" your iPad or iPad 2, you can get tweaks, themes, apps and mods that are not official or endorsed in any way by Apple. Jailbreaking has some benefits, and many of the current features of the iPad derive from jailbreak tweaks. The downside of jailbreaking is, if you dont know what you're doing, it can be very dangerous and ruin your device. Some jailbreak tweaks are also illegal. So YES you can mod your iPad if it is jailbroken.
You can; use the App Store. Alternatively if your iPad is jailbroken you can also use Cydia to download applications that Apple wouldn't ever approve for their own store.
It is possible if you have jailbroken your iPad to install software that allows for external control, file deletion and general bad-things-might-happen. If you are using iTunes to sync your iPad, then no.
Only the cost of your 3G dataplan, including possible overages.
There has not been an iPad virus yet for non-jailbroken iPads. The way that memory is segregated with each application makes it almost impossible for any application to change others or install background applications.