(Not a teacher)
Generally, these terms are only used in formal letters when the adressee's name is not known. Perhaps occupations that function to 'serve' people - waiting tables, customer services etc - use it to be respectful too. The equivalent to 'sir' for a woman in these cases is 'madam'. I can't think of an equivalent for a young girl, and unless the young girl was of very high importance most people would just refer to her by her name (and ask if they didn't know).
The only time I ever used 'sir' in spoken language in my life was in high school, to address male teachers. To address female teachers I would say 'miss'.
'Sir' as a title in Britain - that is, someone with the orders 'Knight Grand Cross' or 'Knight Commander' (that is, has been knighted by the monarch) - isn't anything to do with being respectable. It replaces the 'Mr' in the person with the knighthood's name. The female equivalent of this 'Sir' is 'Dame'.