1. Crystals stay in your inventory until used? They are not discarded end of turn or end of round?Correct. You can't have more than 3 crystals of one color, and no black or gold crystals exist.
2. You can only use one die from the source per turn (barring skills/cards) but you can use as many crystals/tokens as you have available?Correct.
3. When setting up solo conquest it says to use 7 countryside tiles. These are randomly chosen? Not 1-7 shuffled but a randomized 7 countryside tiles?Correct. That's also true for any other scenario.