Is the hacking of an email address containing a website for downloading Islamic books considered a trial from Allah, or a punishment for an action not done sincerely for the sake of Allah?

What your friend did is theft and aggression. He must repent and return your right. Dedicating your website to uploading Islamic books is a righteous deed, as long as there is no Shar'i prohibition in them. Your friend stealing your website does not indicate corruption of your intention; rather, it could be a trial, and we hope that your reward remains continuous if your intention is good.