You're not going to be able to seal Sharpie writing onto a mug that will be used. If it will just sit on a shelf, it doesn't really need sealing either.
As far as the Corian, man, if you're taking a class, ya gotta pay attention!

The fact that it doesn't need sealing is one of the major selling points. And you are displaying the other major selling point right there in your handiwork.

it can be worked (and repaired) with wood tools. Fabricators gotta know this stuff. It helps upsell the customer.