You need a valid official photo ID (e.g. passport, identity card, driving licence).
You do not need an ID card to buy a prepaid SIM card. But if you want to register and activate it at the retailer, you would have to present your ID card. You can do the registration later as well.
Yes, you can pass on or transfer a prepaid SIM card registered in your name to another user. In this case, the card has to be registered in the name of the new user, i.e. the card needs to be transferred.
Please find information about that at the website of your provider or contact the customer service.