Sorry for the late reply.
Is there a 3d Geeks server or does the app speak directly to Thingiverse?
The app uses both, 3D Geeks has its own api for some specific features.
If there is a server does 3d Geeks cache content to reduce load on Thingiverse as well as speed up access for 3d Geeks users?
No, we dont cache anything from thingiverse because I would guess that is against the rules. However the official thingiverse apps uses other calls than 3D Geeks which makes it extremely slow.
Would 3d Geeks backup data in case Thingiverse ever closes down?
Same answer as question 2. We dont cache any thingiverse data, as that would be against the rules.
Is 3d Geeks going to fold in some of the other 3d model sites?
There are some plans on the roadmap, yes.
Is 3d Geeks going to have its own model device like Thingiverse?
What exactly do you mean by model device?
Is 3d Geeks going to add missing functionality like a move function in Collections?
Great suggestion, we have added it to our backlog. Expect this feature soon.
What is the long term vision for 3d Geeks?
We have some really cool plans on the roadmap, in fact we are working on some super cool stuff. But we cant talk about it untill it is done. Since we want to surprise you guys!
Thanks for the interest!