As for shards, I found a bunch in the desert area (where the sandstorm is).
Also, I can confirm the Red Shard move tutor (has mainly offensive moves, such as Ice Punch, Dual Chop, and Seed Bomb) is in Driftveil City. I just made it here, but haven't seen any others. Most moves are about 10 shards. I'm unsure how I had 13 by then, maybe he gave me 10 free ones.
Needless to say, my Huge Power Azumarill shouldn't have Ice Punch this early xD