Hi, welcome to the game!
Tossed enhancements are not considered negated, but the way they are played circumvents the ability on the card, so the ability never activates or resolves in play. You basically sacrifice using any ability on the card to decrease the opponent by X/X, with X = the strength of the tossed enhancement.
Territory class enhancements resolve and are then discarded unless the card places itself in territory or on another card. Cards like this will begin their ability by saying "Place in territory" or something along those lines. Generally though, with TC enhancements you basically use the ability and the card is then spent and placed in discard pile. Characters are different. Territory class on a character just means their ability activates and is active while in territory. Normal non TC class characters only gain their ability when they enter battle, so the TC icon allows these special characters to get their ability when placed in territory as well as when they enter battle. These characters still remain in territory until defeated in battle or removed by a special ability, unlike TC enhancements.
