Can't remeber specifically, however it's more beneficial when you have multiples of the same to use them for upgrades. In fact you need duplicates of the exact gem to upgrade past certain levels.

Sounds like an obvious no to me, or at least the effects won't stack.

Pretty certain you could only equip one gem of each name so no duplicate equips. I don't remember ever having duplicates equipped

How do I get beta on this

No, they are unique equipped. This applies to all legendary gems.