Ich rühre den Reis im Topf um und würze ihn mit Salz und Pfeffer.

In German, many verbs are separable.

• The infinitive is umrühren.
• In the present tense for “ich,” you conjugate the verb stem (rühre) and move the separable prefix (um) to the end of the clause.
  So Ich rühre den Reis im Topf um.

German main‑clause word order goes:

1. Finite verb in second position (rühre)
2. Other elements (objects, adverbials)
3. Separable prefix at the end (um)
   Thus den Reis (object) and im Topf (adverbial) come before um.

Den Reis is in the accusative case because:

• rühren is a transitive verb requiring a direct object.
• Reis is masculine (nominative der Reis), so its accusative form takes den.

Since Reis is masculine and being used as a direct object, the correct accusative pronoun is ihn.

• Nominative masculine pronoun: er
• Accusative masculine pronoun: ihn

The preposition mit always governs the dative case. When talking about substances in general (mass nouns), German commonly omits the article:

• Full dative with article: mit dem Salz und dem Pfeffer
• Natural usage: mit Salz und Pfeffer

Yes. If the context makes clear what you’re seasoning, you can drop the pronoun:

• … und würze mit Salz und Pfeffer.
  Including ihn simply emphasizes that you’re seasoning the rice specifically.

Absolutely. German allows flexibility in placing adverbials:

• Ich rühre den Reis im Topf um. (object + place)
• Ich rühre im Topf den Reis um. (place + object)
  The meaning stays the same, though the element you mention first can receive slightly more emphasis.