Can we omit the 吗 at the end of a 难道 rhetorical question? The Chinese Grammar Wiki writes:


  Note that 难道 can only be used for rhetorical questions which could be answered with yes or no, and generally end with 吗.


And gives examples such as:


  今天是我的生日，难道你不知道吗？


However, none of the examples on 标准教程HSK4上 page 105 include 吗, such as:


  怎么有买了这么多饼干和巧克力？难道你不减肥了？


From the examples I've seen, I'm getting the impression that the 吗 at the end can be included or omitted without changing the meaning.

Question: Can we omit the 吗 at the end of a 难道 rhetorical question?
Yes, definitely you can. However, in some situations, with 吗 it sounds more natural and less rude. And sometimes, with 吗 it might sound less criticizing, such as your first example 今天是我的生日，难道你不知道吗?