What does 你要买点儿什么？ mean exactly? (吗 question vs. Wh- question)
Yes, with or without 吗 could be different.

你要买点儿什么？ -> What would you buy?

你要买点儿什么吗？ -> Would you buy anything?

点儿 doesn't change the basic meaning here. It just means a bit/a little, and makes the mood soft.