Outlook does not come with Office Home and Student.
It only comes with Microsoft Word, Excel, PowerPoint and OneNote,
So the Outlook you have will be a pre-installed trial on the computer.
this is why it keeps asking for the Product Key.
You can either keep entering the Key as you are doing now, if it is allowing you to use it (it will have limited functionality).
Else you would need t purchase Outlook which you can do via the below link.Click Me To View
Or you can you Windows Mail, which is a more basic version of Outlook and is free from Microsoft hereClick Me To View
But it is a trial version you have, as Outlook does not come with the home and student version of Outlook.
If you would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service, that would be greatly appreciated.