Is there a way we could add a default header to all homebrew content? I think that there has been some confusion with some people googling for DnD Races and not knowing that certain races/items are homebrew especially on mobile.

Here you can see there is no disclaimer that this is homebrew and NOT official content.  DnD Beyond is known for having official ties to WoTC so its sometimes hard to convince folks that not everything on the site is official content. 

We could have something similar to the warning on the UA content?

While I agree that there needs to be a designation for homebrew in the character builder, the designation for homebrew is on your screenshot: The little blue icon with the house on it designates homebrew. I do however I agree with you-- there should be something similar to the UA notation, since a single symbol is fine for folks like me who are here all the time, but less clear for folks who don't spend an ungodly amount of time lurking every corner of DDB.