Hearthstone – End Date of the Launch Celebration

The number of cards and the rarity is fixed, the actual cards you get is random.

Rank 20-16: 1 golden common
Rank 15-11: 1 golden common, 1 golden rare
Rank 10-6:  2 golden common, 1 golden rare
Rank 5-1:   2 golden common, 1 golden epic
legend:     3 golden common, 1 golden epic

Additionally you get between 5-25 dust.

The important thresholds are rank 15 and rank 5. On rank 15 you get a golden rare (100 dust), and on rank 5 you get a golden epic (400 dust).

Source

It's randomly selected for each player. Today my daily quest was "Summon 20 minions that cost 5 or more" that I rerolled, getting a "Win 5 matches with Rogue or Warrior". As you can see none of them match the one you got.

Regarding the high number of opponents of the same class it mostly depends on the game mode you're playing, but can also be influenced by the time of the day when you're playing. In Arena you'll find a lot of Paladins, Mages and Rogues, the classes that are currently stronger in that game mode, while on Constructed you'll see many Druids, Warriors and Paladins, that are very strong in the current meta. Also from my experience I've seen that late night play promotes slower decks (I get more Control Warriors or Dragon Priests), while on lunch break or during the day more generally I get faster decks (usually Paladins).