Shadowless cards are experiment cards that were created by the Pokemon card creators as testers and were early models. Shadowless cards have less bold text and have no drop shadow under the character illistration window (which gives it the cards' name). These cards are extremely rare which makes them much more valuable.
The card to the left is a shadowless card and the one to the right is not. Notice how the shadowless one has less bold text and no shadow:
Mint means that the card is new, original, unused, and appearing to be unused. AKA in very good condition. Because they are new, unused and in good condition they are usually more valuable. Its very obvious to tell the difference between mint and damaged and old so I'm not going to post a picture. But hope I helped.