Touching the Qur'an without wudhu

Q: Is it permissible to touch a mus'haf without performing ablution/wudhu? Or let's say is if permissible to study qur'an without wudhu? Because I am memorizing Qur'an and I always go to the comfort room, always pee so I find it hard to make a wudhu every after entering the comfort room. It is also very cold in my country especially in morning. But if it is impermissible or not permissible then I will have no choice but to make wudhu every time after entering the comfort room.

Revocable divorce

Q: My husband has written out a talaaq-e-rajee stating his granting it and our id numbers, date and time. Is it valid and do I start my iddah now? Do I take the letter to the Imam who married us to confirm?