not normally a "the" situation. normally school as a general thing, but it could be that you are asking about a very specific school rather than school as a general idea. When does (something) (happen) is used to refer to a regular and/or repeated condition, an always true thing. When will (something happen) is usually used for a specific situation (like today, or tomorrow, and you don't care when it would usually or typically open, but specifically when it will open tomorrow or whatever time you mean).
reopen and open don't matter which you should use. reopen does presume a singular (punctual) event though, so I would use will.