Can u put something on corion counters to make them shnier?

I don't think so.
Corian is a form of plastic. Its sheen comes from polishing. In other words the finer you sand it the more it shines. Don't remember the recommended procedure but I would sand to about 600 to 1200 grit and then use a polishing compound.

Would no recommend waxing or the application of any type of surface material. Don't think any type of surface material would stick.

Use white polishing compound. Always use something under pots, pans, knives with Corian, it is a fairly soft material.