Hi winymse,
Welcome to the board!

I'll do my best to answer your questions.
1. No, it's not rude to print off and send your own photos of the celebrity. It's actually probably the best thing to do, as not always does the celebrity have photos on hand that they can sign for you. Especially when sending via venue (to a movie set, concert venue) printing off your own photos is the best bet.
2. No it's not rude to request two separate photos signed. Just state in your letter that, like in your case your cousin is a fan also and it would mean a lot to you to have a 2nd photo signed for him/her. You can send together, sometimes it's better to send individually though.
3. You can, but I wouldn't suggest it unless you hadn't received your request back in many months or over a year from the first address you sent to. It's not really rude to send more than one request, but you must remember that there are MANY others that are probably trying that exact same celebrity so be diligent as to how many requests you sent out so you don't ruin it for others who are just as big fans as yourself.
4. For your envelope TO the UK you use the required about to send internationally and in the same package you will include your IRCs for your SAE (which is the return envelope).
I hope that answers all your questions. Don't hesitate to ask more.
Larisie