Learn Turkish: Evi hasarsız teslim etmek üzere anlaşıyoruz. - We are agreeing on the condition of delivering the house undamaged.

You are right that -mAk üzere often means "about to do something". However, when used in agreements, promises, or when giving something, it acts as a proviso clause meaning "on the condition of" or "with the understanding that". Here, teslim etmek üzere sets the strict condition for the agreement.

Why is the accusative case used on evi?

The suffix -i marks a specific direct object. The speakers are agreeing about a specific house they are handing over. If they used the plain noun ev, it would mean delivering houses in general, which doesn't fit the context.

Hasarsız means "undamaged". Why doesn't it need an adverb ending to describe how the house is delivered?

In English, we often add "-ly" to turn an adjective into an adverb. In Turkish, you can usually place an adjective like hasarsız (created by adding the "without" suffix -sız to hasar) directly before a verb to describe how the action is done, without needing any extra grammar.

Why use the compound verb teslim etmek instead of a single word for "deliver"?

Many Turkish verbs are formed by combining a noun with a helper verb like etmek (to do/make). Teslim means "delivery" or "handing over", so teslim etmek literally means "to make a delivery".