Yes, it’s all possible. Look at the Target Attribute for getting the thumbnail to open in a new page.
Will you have users categorize videos when they upload them? (less workload for you) or will you personally determine each videos category?
In my opinion this won’t be a simple project. There are lots of routes you could go. If it was me, I’d use PHP with a MySQL database.
I do something similar here with pictures: http://www.proximitycast.com/aGem/all_photos.php
You can see my Gallery by Category selector at the top right of the page.
I’m not really happy with how my categories are at this time. It’s an improvement I need to get around to doing sometime hopefully in the near future.
Good luck, hope this helps! But, yes it is all possible…