Ah good question. The tiles on the board are face-down. When you mine a tile, it gets added to your hand and its type is revealed. Similar to a card game, you can see what's in your hand, but you can't see what's in your opponent's hand (only how many tiles your opponent has).
| Stone tile | Rune tile |
 |  |
I'll update the description with that info.
Also, as far as the distribution, Rune tiles have the same probability of finding a face card in a standard deck of cards (Stone tiles = 2-10). I tried to make it so you could theoretically play this game with a standard deck of cards and a set of chess pieces (you'd need something for a 7th piece though since chess only has 6).
I'm not sure I understand your question about the AI killing its own Forgekeeper.