No.
You cannot install this Beta unless you jailbreak your iPad. This Beta is only available to developers, and being sold illegally for hackers. If you jailbreak, you'll be locked out of the app store and alll the other updates that will come before it is released this fall. Be patient.
no
Yes, you can.
iPads run on iOS
Yes. iOS 5.1 is jailbreakable, search the internet for it.
If you have the iPod Touch 3G or 4G (current one), an iPhone 4 (not the iPhone 4S) or iPhone 3GS, or the original iPad (Not the iPad 2) then use redsn0w 0.9.10 to jailbreak. If you have an iPad 2 or, iPhone 4S, you cannot jailbreak it on iOS 5.0.1 yet
The ipad 3 will be jailbreakable but you have to wait for th IOS 5.1 jailbreak to come out
ios 8 can be installed on ipad by first registering or have your device UDID registered by a developer and then download the iOS 8 beta and install it on your ipad
Yes. All iPad minis should be running iOS 6 and can update to iOS 7 this fall.
iOS 5.1 untethered jailbreak
Yes, you can use Absinthe 2.0.1 to jailbreak iOS 5.1.1. Here is a website with step-by-step instructions on how to jailbreak: http://www.redmondpie.com/jailbreak-5.1.1-untethered-iphone-4s-ipad-3-ipod-touch-and-more-using-absinthe-2.0-video-tutorial/
A jailbreak tool called evasion has been released with works on all iOS 6 and iOS 6.1 devices - iPhone, iPad, iPad mini, and iPod touch. This is an untethered jailbreak, which means that you won't need to reapply it after reboot. In practical terms this means that a flat battery won't remove your jailbreak.