Learn Turkish: Dünkü krizden sonra, istihdamı azaltmış olan şirket kapandı. - After yesterday's crisis, the company that has reduced employment closed down.

You could, but it changes the timeline. The standard -An suffix in azaltan usually implies an ongoing or general action ("the company that is reducing employment"). Using -mış olan explicitly shows that the reducing was completed before the company closed. It acts like the English perfect tense: "the company that has reduced" or "had reduced".

Why does the verb azaltmış take the accusative object istihdamı (employment) here?

Because of the causative suffix -t. The base verb azalmak is intransitive and means "to decrease" or "to become less". By adding -t, it becomes azaltmak, a transitive verb meaning "to reduce [something]". That "something" is the definite direct object, so it takes the accusative ending -ı to become istihdamı.

Why is it dünkü krizden and not just dün krizden?

To say "yesterday's crisis", you need to turn the time word dün (yesterday) into an adjective. In Turkish, you do this by adding the suffix -ki, which becomes -kü here due to vowel harmony. This allows dünkü to directly modify the noun kriz.

Why is the verb for "closed down" kapandı rather than ?