Learn Farsi: پادشاه به خادم خود پاداش داد.

The word خادم (khâdem) follows the Fâ'el (C1-â-C2-e-C3) pattern. Its root consonants are kh-d-m, which relate to serving (as seen in the noun خدمت, meaning service). This morphological pattern creates an agent noun, meaning the 'doer' of the action, so a خادم is one who serves, or a servant.

Why does the sentence use خود for 'his' instead of the possessive suffix ش?

Because the possessor (the king) is also the subject of the sentence. In Farsi, when the subject owns the object, you must use the reflexive pronoun خود. If you used the suffix ش and said خادمش, it would imply the king rewarded some other person's servant.

Why is the preposition به used before the servant instead of the direct object marker را?

The verb پاداش دادن is a compound verb that literally translates to 'to give a reward'. Because you are giving a reward 'to' someone, the person receiving it acts as the indirect object and requires the preposition به. You would only use را if the servant were the direct object.

Is پاداش also an Arabic participle?

No, پاداش (pâdâsh) is a native Persian word meaning 'reward', so it does not follow Arabic root-and-pattern morphology. A quick trick to remember this is that it contains the letter p (پ), which does not exist in the Arabic alphabet.