Ev çok dağınıktı; temizlik ekibine mutfağı temizlettim.

The semicolon links two closely related independent clauses: a reason and a result. You could also use:

• A period: Ev çok dağınıktı. Temizlik ekibine mutfağı temizlettim.
• A connector: Ev çok dağınıktı, bu yüzden temizlik ekibine mutfağı temizlettim.
• Or put the reason second with çünkü: Temizlik ekibine mutfağı temizlettim çünkü ev çok dağınıktı.

The cleaning crew did the actual cleaning. In a causative with a transitive verb, the person made to do the action (the causee) is typically in the dative:

• temizlik ekibine = “to the cleaning crew” (the causee)
• mutfağı = the direct object (the kitchen)
• temizlettim = I caused/made them clean it.

In causatives:

• If the original verb is transitive (like temizlemek “to clean”), the causee is usually in the dative: Ali’ye kitabı okuttum.
• If the original verb is intransitive (like uyumak “to sleep”), the causee becomes the direct object: Çocuğu uyuttum. Here, temizlemek is transitive, so temizlik ekibine is dative.

Temizlik ekibi is a noun–noun compound (“cleaning team”) where the second noun takes the 3rd-person possessive marker -(s)i: ekip → ekibi. When you add a case suffix to a possessed/compound form, you also add the buffer -n-:

• ekibi + -e → ekibine Saying temizlik ekibe drops the compound marker and is ungrammatical in this meaning. You could say ekibe alone, but it’s vaguer (“to the team”).

Because it’s a specific, definite direct object: the kitchen. In Turkish, definite/specific direct objects take the accusative:

• Definite: mutfağı temizlettim (I had the kitchen cleaned)
• Indefinite/non-specific: mutfak temizlettim (I had a kitchen cleaned / had kitchen-cleaning done — unusual unless context supports it)

It softened: k → ğ before a vowel-initial suffix. Also, 4-way vowel harmony chose -ı for the accusative. So:

• mutfak + -(y)ı → mutfağı

Yes, Turkish is flexible, but the neutral order keeps the verb last and places known information earlier:

• Neutral: Temizlik ekibine mutfağı temizlettim.
• Object focus: Mutfağı temizlik ekibine temizlettim. (emphasis on the kitchen) Placing the object after the verb (e.g., Temizlettim mutfağı) is marked/colloquial and usually used for afterthought or strong emphasis.

Yes, but that’s passive voice: The kitchen was cleaned by the cleaning crew.

• Your original sentence is causative and foregrounds your agency: I had the kitchen cleaned (by the crew).
• The passive removes you as the causer and optionally introduces the agent with tarafından.

temizlettirdim is double causative: “I had someone make someone else clean.” Use it when there’s an extra layer of causation:

• Müdüre temizlik ekibine mutfağı temizlettirdim. = “I had the manager get the cleaning crew to clean the kitchen.”