"Shall I" is common, in my experience, in Britain. It's used for a polite offer and means the same as "Do you want me to". Here are some natural situations: Shall I meet you at 8pm Shall I open the present for you? Shall I go first? Shall I be mother? (funny expression for when you offer to pour the tea / coffee, or serve food to others during meals) Shall I do the honours? "Should I" = "Is it a good idea for me to..." e.g. Should I climb Mount Fuji in December or not? Should I speak to you later (if you are busy now)?

yes it's right I think "Should I~~~~" is more used and common also May I .... is more politely for asking