Learn Dutch: Hun inzending is uitstekend, dus de universiteit biedt hun een contract aan. - Their submission is excellent, so the university offers them a contract.

They have different grammatical roles! The first hun is a possessive pronoun meaning "their" (hun inzending = their submission). The second hun is an object pronoun meaning "them". In formal written Dutch, we use hun for "them" when it is an indirect object without a preposition, like here where the university is offering a contract to them.

Could I use hen instead of the second hun in this sentence?

In strict formal writing, no. Because they are the indirect object receiving the contract, and there is no preposition like aan before them, you must use hun. You would only use hen if they were the direct object, or if you included the preposition, saying biedt een contract aan hen. In everyday speech, however, many Dutch people mix these up or just use ze.

Why is aan at the very end of the sentence?

It is part of the separable verb aanbieden (to offer). In a main clause, the conjugated part (biedt) takes the second position, and the prefix (aan) gets pushed to the very end of the clause.

After dus, why is the word order de universiteit biedt rather than inverting the subject and verb?