Learn Arabic (Modern Standard): صهرهم رجل ذكي ومجتهد. - Their son-in-law is a smart and hardworking man.

While translated here as son-in-law, صهر broadly refers to any male relative by marriage. Depending on the context and regional usage, it can also mean brother-in-law or father-in-law.

Why is there a و (and) between the adjectives ذكي and مجتهد?

Unlike English, which can stack adjectives right next to each other before a noun (a smart, hardworking man), Arabic places adjectives after the noun and generally connects them with the conjunction و when there are multiple traits describing the same noun.

The subject صهرهم is definite, but رجل is indefinite. Does this difference in definiteness matter here?

Yes, it creates the invisible English is. In an Arabic nominal sentence, the subject is typically definite (here, made definite by the possessive pronoun هم), and the predicate is indefinite. This definite-to-indefinite shift tells you exactly where the equation happens: Their son-in-law [IS] a man...

If I were reading this with full case endings (I'rab), what case would the final word مجتهد take?

It takes the nominative case with an un ending (مجتهد - mujtahidun). This is because it is linked by و to the first adjective ذكي, which must agree in case with the nominative predicate noun رجل (rajulun).