This depends. First off, it would need to be an AT&T model, as Verizon models do not use a SIM card. Also, it depends on the UK carrier. Most would be compatible with AT&T's network, so yes, you should be able to use a US iPad 2 with a UK SIM. Although, take note that the iPad uses a microSIM, so the UK SIM card will have to be cut down to fit into the iPad.
No.
no
No u can not
The iPad made life easier because the iPad has apps that help you with homework you can listen to music,play games the iPad 3 is not that very great my mom said that this iPad, when you use it a lot the bottom of it burns the iPad 2 works when you use it a lot Plus the iPad 3 cost $500 And the iPad 2 is $400
Apple does not make iChat for iPad. But if you have an iPad 2 or newer, you can use FaceTime which is very similar to iChat.
You can use an IPad 2 with no carrier at all if you only use the wireless internet with it or wifi. You can use AT&T or you can use Verizon or just wireless internet.
You can't you need iTunes.
Yes
Yes, but it will be a bit floppy. You will want to put some foam or rubber inside to hold it in place, since the iPad 2 is thinner.
u plug them in
Both the iPad 2 and New iPad (3) use the same smart cover. They are $49.00 for the neoprene ones, and $79.00 for the leather ones in the US.