They are not the same. "Do you know what?" looks like a question but is not. It is just a way to try to make somebody curious about what you are about to say. It is the same as "guess what!"

非正式交流就不用考虑那么多语法问题了，只要没有误解就OK。

I’d say not exactly because it feels unnatural. It’s even more common for us to say, “You know what?” in that context. “Do you know what?” is still okay. But “Do you know?” isn’t the right choice for that. You can only use the latter (Do you know?) if you first said “I feel the same” and then followed it by saying “Did you know?”.