When I get crystal rewards (for example via rolling dice after winning in some adventure sites), do I forfeit them if I already have 3, or can I reroll?
Effectively, you're forced to use the new crystal immediately. You gain a mana token of the crystal's colour directly into your Play area.
From the rules, page 5, under "Gain" Effects:
If an effect tells you to gain a crystal, take a mana token of the corresponding color and put it in your Inventory. If you already have three crystals of that color, gain a mana token of that color to your Play area instead.