They are both grammatical sentences in English - However, they are used in different contexts. "Did you see his lunch box" is more likely to be used to refer to something in the past that does not necessarily have any connection to the present. For example, you might ask someone: "Did you see Johnny's lunch box last Tuesday? Wasn't the Iron Man design super cute?" However, if you use "have you seen his lunch box," you are implying that this question has continued importance in the present. In the specific context you mentioned (your son lost his lunch box and you want to find it, so it is *relevant* to the *present*), I would ask "have you (by any chance) seen my son's lunch box? He seems to have lost it!" There is no difference in terms of politeness between the two, but they are different grammatical constructions used in different contexts. To make the question less abrupt and therefore more polite, add "by any chance" to soften the potentially accusatory sense of asking someone if he knows where a lost item is. So "have you by any chance seen my son's lunch box" is the best way to ask the question, given the circumstances. :D Hope this is helpful.

Either is fine.

Have you seen."Have you seen" is more generic, "did you see" is used in cases like "when you were in the classroom, did you see it [at that time]?"

Have you seen.....?