Learn Polish: Szanuję jego mądrość.

It is formed from the adjective mądry (wise). To create the abstract noun, we drop the adjective ending -y and add the suffix -ość, giving us mądrość (wisdom).

The verb szanuję requires the accusative case. Why doesn't the ending of mądrość change?

You are right that szanować takes the accusative case. However, mądrość is a feminine noun that ends in a consonant. For all feminine nouns ending in a consonant, including all those formed with the -ość suffix, the accusative form is exactly the same as the nominative form. Therefore, it stays mądrość.

Could I use the reflexive possessive pronoun swoją instead of jego in this sentence?

No, because swoją refers back to the subject of the sentence. The subject here is 'I' (implied by szanuję). If you said Szanuję swoją mądrość, it would mean 'I respect my own wisdom'. Because you are respecting someone else's wisdom, you must use jego (his).

What is the infinitive of szanuję and what pattern does it follow?

The infinitive is szanować (to respect). It follows the very common pattern where verbs ending in -ować in the infinitive change that ending to -uję, -ujesz, etc., in the present tense.