At the hotel
Your hotel may ask to keep your passport for the time that you remain a guest; this is normal procedure. Hotel administration needs it for daily reports to the police. Don't worry, it will be safe there! Besides, you don't need to carry your passport on you when you're out, you basically need it only at the time of entering and exiting the country.
If you're travelling with your partner but are not married, no questions will be asked. You can occupy one room. The rule of having a marriage certificate to stay in 1 room at the hotel applies only to the locals.
At an average Iranian hotel you will always find a bathroom with a toilet and a shower. However, expect that you will only find a squat toilet at cheaper hotels. Breakfast is usually included in the price of your stay, as well as room service. Regular 220V electricity sockets are used.
Tips to the porter, janitor and waiters will be appreciated.