Why is a group of fish called "school"?
And is it anyhow etymologically connected with the word "school" denoting an educational establishment?
A group of fish can be called a school or a shoal. Both words from the Dutch root "schole" meaning a troop or a crowd.
From Etymology Online:
"group of fish," late 14c., scole, from Middle Dutch schole (Dutch school) "group of fish or other animals," cognate with Old English scolu "band, troop, crowd of fish," from West Germanic *skulo- (source also of Old Saxon scola "troop, multitude," West Frisian skoal), perhaps with a literal sense of "division," from PIE root *skel- (1) "to cut."