Can I create a false ceiling using XPS board instead of gypsum board?
XPS must be covered with drywall or another fire resistant material.  XPS, when exposed to heat will put off toxic fumes and will melt.  The last thing you want in a class room is molten foam melting onto students in the event of a fire.

Stick with proper ceiling tiles, drywall or another suitable material.  What you are proposing would be against most building codes that I know of, at least in North America.