They ban iTunes etc because technically you're only supposed to use the internet for work. ie you're really probably not supposed to use it to check the news, or go on facebook, or whatever. iTunes is a more conspicuous non-work use, and I think that's all. I use iTunes at college but save my downloading of music for the holidays (because I'm so reliant on my internet that I'm paranoid about losing it). No-one's got in trouble for using (eg) YouTube as long as they've stayed within the bandwidth/download limits, and that's clearly not work either, so... I dunno. Make your own decision. Since it's legal etc you probably wouldn't be in a lot of trouble even if they caught you.
I have not the foggiest what the whole no power splitters thing is for, chaps. I'd never encountered it before. A guess would be that once when I was in my first year a guy's room caught fire and it turned out to be due to electrical equipment - but it was more that he had incense burning on top of his fridge than anything about adaptors and so on. By the way, there will search your room once a term for anything you're not supposed to have - eg toasters or candles. I had a fish for three terms before they discovered it (or at least before anyone made a fuss) so they're not very thorough, but they will find eg candles if you leave them out on the side. Then you just get a note left on your bed saying "you've got candles and you shouldn't" and a either little fine, or if it's blutack they often just say "take it down and I'll be back to check". By "little" I mean one of my friends was fined £15 for having a candle that had clearly never been lit...
They do sort of check electrical appliances if you leave them in communal kitchens - eg toasters or microwaves, if you've bought them yourself and left them in communal areas, will get checked when the college electrician comes round. Never heard of anyone being asked to pay for it. Think they're just covering themselves for the right to get rid of something if the college electrician thinks it's dangerous, even if it's not college property. Never seen it done for electrical items in someone's room (even the infamous fire-causing fridge - though that was a melted wreck by the time they got it out).
ETA: Medical forms - I think you give those in some time in freshers' week when they register you for the college GP. You have the world's tiniest medical exam in which they basically just take your blood pressure, and hand over the form. I think. Have a good check for dates but if in doubt, there's very little you HAVE to have sorted out before you come to Oxford; most of it you can worry about when you arrive.