Character select in arena

When you enter the arena you are given 3 random champions to select from. I was wondering:

• Are these heroes truly selected at random?
• Does the game give everyone the same 3 heroes on the same day?
• Is there a rotation in order if this is the case?
• If I enter the arena and I hate the Heroes I am given, will they ever reset if I don't select one?

The classes available in the arena, as well as the cards available when constructing your deck, are both entirely random.

Once you "Buy-In" to the Arena, you are locked to those options until you win 12 times, lose 3 times, or retire. Your status in the Arena is otherwise saved in perpetuum.