For the first two categories, the price usually includes breakfast. Most hotels have restaurants and offer a variety of meal plans ranging from only breakfast to full board.
Payment is generally in cash but major hotels accept credit cards.
Hotels are rated with stars. The most common ones have three stars, the most luxurious have five. The clerk will need a form of identification from everyone checking in, they will keep this form of identification for the duration of the stay. Note that especially in tourist areas individuals will place themselves near bus stations or train stations advertising rooms for rent in their own homes. Unless one knows Romania very well, it is better to avoid such situations and head for a hotel.