Maybe she didn't want to commit to a large role and was happy to do the part given it was filmed in the UK anyway and wouldn't have involved a lot of travel. But it does highlight the thought that goes into casting that they can get a high profile actor even for what some might say was small role.
I'm betting that they didn't kill her, mainly because I don't think that they cast Emilia Clarke just to kill her off. I think that at the beginning of ep. 4 we'll see here sit up, open up her shirt/blouse to reveal that she had body armor underneath. Hollywood loves the bullet proof vest reveal trope and I was fully expecting to see that trope at the end of ep .3. But I'd be just as happy to see that she was actually killed because it's become such a trope for characters to appear to have been shot and killed only for it to be revealed that they were wearing body armor all this time.
Not really a spoiler, but unless they're swerving us, there were several scenes in the trailers that have her in them that haven't appeared yet.
I think it has more to do with the fact that Carol, Ms Marvel, & Photon are all imbued with their powers, but G'iah simply has access to them at will. Kind of like their power is in their DNA, but she can effectively change her DNA.
As Usagi said, G'iah doesn't permanently manifest them, she can just tap into them at will.
Technically any hero with control of their power taps into them "at will"..
I think the difference with G'iah is that she has to shapeshift that aspect of Carol's DNA to the fore in order to tap into that power. In the same way as she tapped into Drax's DNa to manifest his arm or the Frost Beast's DNA for the ice blade.
