[Polkageist]

Since it sounds like you're defining the rules of the game world, the answer to all your questions is 'Yes'

GURPS is generic, so it generically uses the term "demons" for evil extradimensional baddies. If in your world there are "elder things" instead of "demons" then you'd define for your game the various spells that interact with the generic "demon" descriptor as working on "elder things" just swapping out the world 'demon' for 'elder thing'.

Now if BOTH kinds of entities exist in your world, then specializing spells, powers, and skills is appropriate, and where a specialized variant for Elder Thing vs. Demon doesn't exist then that particular power/spell/skill isn't applicable (or heavily defaulted, whatevs). This saves time since you don't have to write new mechanics, you can use the existing spells/powers/skills mechanics and put (Elder Thing) next to it so you know that it only works on Elder Things.

It would definitely be cool to be able to summon the more dimensionally weird things. Fishmen are pretty corporeal, but Shoggoths would be cool to pop out of a rip in the fabric of reality. I would just use the Summon spell since the mechanics are tuned for that kind of action, and specialize it like Summon (Elder) vs. Summon (Demon), no defaults from one to the other, same costs & prereqs and since it's obscure/arcane figuring out where you can learn it to justify points in it is a challenge.

Same thing with the other entity-interacting spells. Specialize by putting the spec in parentheses and allow/disallow defaults as you feel appropriate. As for the Elder Symbol being important, that's just set dressing but a good one so putting the descriptor into the specialized description is aces. To help you sort your decision as to whether protection/containment spells work on Elder Things, you mention that protective/control spells are already specialized for other entities. I would, for consistencies sake, advise treating the Elder Thing specialization with the same limits as the other entity specializations, including defaults and penalties for using the not-quite-right protection/control spell. IF Elder Things are supposed to be extra hard to deal with then you can increase penalties or not allow un-specialized protection/control spells to work on them.