"I wonder why I feel so hungry" or "I wonder why I feel so alone", they are good enough to be understood.

Both are fine. The "do" can be omitted or not. If present, it could serve as emphasis.

Thanks :)

You may find this page useful for learning all the rules. http://www.edufind.com/english-grammar/question-forms-and-reported-speech/

It is wrong to include the "do", and in an exam it will be marked wrong.