These are special champions, which you obtain through various means: Some are just lucky (they are in the champion pool that it uses at fame levels), some are from certain quests. I have 3 of them so far, 2 from luck and 1 from a quest.

There's a thread around here somewhere that lists how to get them, but I think it's more fun to find them as you play. So just keep playing and you should encounter them sooner or later.

No and no. If you skipped quests close to your starting point, they will still be easy/medium when you do them later in the game. Quest maps closer to home also provide easier quests than when you start them far from your starting location.

Random events are just that: random. They do not always take place.

If you love to do quests, select the 'Wanderlust' trait. If you don't mind exploiting the mechanics, it saves a faction trait point if you select Altar as one of your opponents and buy quests from them.