Learn Icelandic: Samstarfsaðilinn mun hafa sent honum bæði lokaskýrsluna og matið. - The partner will have sent both the final report and the evaluation to him.

It matches the English structure perfectly. You use the conjugated future auxiliary verb munu (here, mun for the third person singular), followed by the infinitive hafa, and finally the supine form of the main verb (sent).

Why do the objects in this sentence take two different cases (honum vs. lokaskýrsluna and matið)?

The verb senda takes two objects and dictates their cases. The recipient (the indirect object) is in the dative case, which is why we use honum. The things being sent (the direct objects) are in the accusative case, giving us lokaskýrsluna and matið.

Does the word bæði change its ending to match the nouns lokaskýrsluna and matið?

Not in this context. While báðir/báðar/bæði can be a declinable pronoun meaning both, here it is used as part of the fixed conjunction pair bæði ... og ... (both ... and ...). When used this way to link sentence parts, bæði acts as an invariable particle and does not decline.

What is the makeup of the compound noun samstarfsaðilinn?

It is built from samstarf (cooperation or collaboration) and aðili (party, person, or participant), joined by a connective -s-. The -nn at the end is the masculine singular definite article, making it the collaborating party or the partner.