For my brother, an expensive dress and a good-looking dress are one in the same.

Correct sentence: For my brother, an expensive dress and a good-looking dress are one and the same.

The phrase "one and the same" refers to something that is the same as something else.

The feud between the Johnsons and the Davids, two families each with a deep-seeded hatred for the other, is a well-known story in the whole city.

Correct sentence: The feud between the Johnsons and the Davids, two families each with a deep-seated hatred for the other, is a well-known story in the whole city.

The phrase "deep-seated" refers to something (such as a belief, feeling, idea, or behavior) that is deeply ingrained in something else. The phrase "deep-seeded" may sound like it makes sense, at least from a metaphorical point of view, but the phrase is incorrect.

Having spent the last several months in finding the evidence, the attorney said to the defendant, "There’s nothing more we can do. The ball is in court."

Correct sentence: Having spent the last several months in finding the evidence, the attorney said to the defendant, "There’s nothing more we can do. The ball is in their court."

The phrase "the ball is in your/their court" means, figuratively, the person or persons being referred to (the subject of the "your" or "their" reference) must make the next move or take action next. In this sentence, the attorney has established that there is nothing further his team can do. He emphasizes this by using the idiomatic expression, suggesting that they must await action from someone else.