You could use either, but 'shall' is better if you are just making a suggestion, whereas 'should' implies that there might be some reason why it wouldnt be a good idea. So 'Are you thirsty? Shall I make you some tea?' But 'Should I make you some tea? Or do you have to leave soon?' But we often use 'should' and 'shall' interchangeably in the first sense

Shall I make you tea? Should I make you tea? . "i' --> "I" First person singular pronoun, gets a capital letter. Always :)

Никакой разницы нет.