I probably do not quite get the meaning of "partner for school" (is it a mate sharing the same bench in shool? or a tutor who helps in studies?) - if so, none of this exists in Polish.
"Partner" (male noun) means:
A person with whom one does something together (dances, plays a game, has a conversation, starts an enterprise, drinks alcohol).
An actor who is playing on a stage as a supporting actor to another one.
A person with whom one has a relationship (busines, sexual, etc.): "On jest moim partnerem biznesowym" [He is my business partner (contractor)]; "On jest moim życiowym pertnerem" [He is my life partner] - but this is a very formal expression, so in everyday situations it is rather avoided.
Someone who has a status, competences or powers equal to someone else.
Attention: "partnerka" (female noun) is used only in the first 3 meanings. In the 4-th meaning male noun is used even if related to a woman: "Anna (female name) okazała się twardym (male adjective) partnerem (male noun) w negocjacjach' [Anna proved to be a tough partner in the negotiations]. Due to this, in the business relationship (3-rd meaning), a male noun "partner" can be also applied to a woman to stress her equality in the partnership.
Attention2: Expression "Być dla kogoś partnerem" [to be a partner for somebody] indicates directly the 4-th meaning. In negation, it has a specific nuance: one who "is not a parther" has lower competences, so: "On nie jest dla mnie partnerem" [He is not a parther for me] means that he is weaker than me, while "Je nie jestem dla niego partnerem" [I am not a partner for him] means that I am weaker than he.