Dealer Trials are a way to earn Car Credits. A Race Ticket is used for each race, and it replenishes over time.
Every time you complete a Dealer Trial race you earn Affinity which is a measure of your relationship with the Dealer. Building up your Affinity gives you the chance to race for different types of cars with that Dealer.
Dealer Trials allow players to select the car they want to win. As shown by the Event Panel, the restriction (the car the player has to use) is OPEN - they can use anything.