I had an interview for a internship last week. They told me, I will get the internship and I will get an email from their recruting manager "the next days". Now 9 days have passed and I haven't recieved anything so far. The internship should start (if they choose the time span I wrote into my application)
Should I (is that professional?), and if yes, how should I ask them about that mail (containing an official confirmation and more detail, when I should start, when I should come to work etc)?
If you've been told you are getting the internship, you are perfectly fine in contacting them asking for the details, especially if the start date is due soon.
If the feedback at the time was positive but sounded like a yes rather than a definitive answer, you can still contact and ask for an update. Bear in mind though that no response may be the answer, it can happen.
You'll likely find there's been an issue/typo with email address, you should be proactive in following up.
When I interviewed for me current position, I was told to expect an invite to an on-location interview after a phone screen. I didn't get anything, turns out there were technical issues in delivering the email.
It happens.
