1. So, what is this type all about?
This type largely originates from two elements, the Crystal Onix from the Orange Islands arc of the Original Pokémon animé series:
The primary inspiration behind this type is the general failure of Rock-type, particularly when it comes to showcase different rock types besides volcanic rocks, such as granite or magnetic rocks. As such, the only Rock-types that have crystals on them are Carbink and Diancie, whereas there are several Pokémon from other types with crystals on them, particularly in Psychic.
2.Where does this name come from?
3. Does this type have an in-game source?
Sort of. Both Power Gem and Diamond Storm are based off crystals, and are learned by Pokémon who have or composed of crystals.
The Crystal-type in TCG is also an inspiration.
4. What would be the ideas behind such a type?
There are three concepts this type can use;
1. Crystals as a general notion for all jewels. So, in this case, ambers and pearls can also be considered "crystals", so could gold and silver.
2. Scientific depictions of crystals, which is immensely rich.
3. Crystals as mystical power sources, which would be primarily inspired by the concept of crystal healing and depictions of crystals in JRPGs such as Final Fantasy.
5. What would be the type interactions of such a type?
Crystal as a type on its own is speculated here and here.
Crystal as a pseudo-type is characterized in Pokémon Azurite, where Crystal is a form-exclusive type that has no type interaction besides having STAB.
6. What would be the distribution of such a type?
Probably very rare, if it is created to be a powerful mystical type, or uncommon, if it is closer to Steel-type.
7. Future comments:
Because Rock-type does not have any major subsection of Crystal-based Pokémon, and all crystal based Pokémon are better off with other types besides maybe some Ice-types, this type has low chance to be conceptualized in near future, unless a radical amount of Crystal Pokémon is announced, a la Dark-type.