My school is really good. (another option?)
That would be a translation to "Το σχολείο μου είναι πραγματικά/όντως καλό", but I guess there wouldn't be such a big context issue.^.^
Hm, I think "really" has two meanings -- "in reality" (which is what I think your sentences mean) and just as an intensifier, a synonym of "very".
Exactly as Philip said. Certainly in American vernacular really and very can be used as complete synonyms.
Σχολείο is pronounced here as if it was written Σκολειο. Is it okay if I do that as well? I find it easier to say "Skolee-o" than to pronounce it "S-kh-olee-o" (which sounds a bit Klingon to me ;-))