Quite close!
"Dear Madeleine,
Thank you for your answer. I will send you my job references."
If the job references are part of the email, then use "I am sending you my job references", or "Please find my job references included in this email." Unfortunately, "I send you" is simply awkward and clunky.
"I am still waiting for the "arbeitszeugnis" from the company for which I am working at the moment. I expect to receive it next week, upon completion of my internship.
My earliest start date is 22.04.2014"
The sentence that was in parentheses wasn't terribly wrong, but just a little too colloquial. I've rewritten it in a professional style. Is it suitable to call the "employment reference letter" an "arbeitszeugnis"?