Use of 放 in 放学 to mean school?
放 has many meanings

放 http://www.cantonese.sheik.co.uk/dictionary/characters/862/
[1] let go; release; set free
[2] let out; dismiss; take leave
....

学 in 放学 short for 学校 (school)
放学(school out) simply means  'be let out of school' or 'be released from school '
Examples for 放 as 'release ; let out':

放监 = be released from jail

放工 = be released from work

放假 = be released for day off; take leave for holiday