OK. I don't know the answers to all your questions but I will have a go :::
1 Any tablet should already have an operating system loaded. My Samsung Galaxy TAB two has Android.
2 Yes they come with a mains cable....sometimes they can be charged up
via a USB socket.
3 How will it work if you don't have an internet connection ? At home you will pick up your home broadband, in the same way as a laptop or smart phone. Away from the home it will pick up whatever Wifi it can detect, like McDonalds or Wetherspoon Pubs, etc. You might have to use a dongle to pick up service if you are not within range of any Wifis. But bear in mind an awful lot of places have Wifi these days, including airports. Tablets are really just a different kind of laptop, that's all.
4 It might seem tempting to buy a tablet in the States but it might not be much cheaper ( taking into account exchange rates ) and you might get caught bring it through Customs and have to pay duty. Also it might not be the same spec. as a British one, and there is the usual difference in mains voltage. God only knows what would happen if something went wrong and you had to take it back to the shop ! Personally I wouldn't bother...just go to Tesco, or another place you trust.
Don't forget it doesn't have to be an Apple Ipad. As I said before, I have a Samsung Galaxy TAB and find it very good. There are others as well and they are ALL cheaper than Apple. For instance, Apple sell a smashing-looking laptop but it costs nearly £2000 ! Its a lovely bit of kit but such an awful lot of money.
I mentioned before that tablets are like laptops but they are not the most user-friendly when it comes to typing lots of text, so bear that in mind. A laptop is really the only one to use in that situation....typing on a virtual keyboard will drive you MAD !
Hope this helps !