4. The probability of an electron being in a given position is determined by it's probability wave function which has a value for every position in space at any one time but it's actual position is only determined when it is measured and the wave function collapses (but then it will be in a specific place). Or are you referring to the double-slit experiment? That shows that the particle's wave interferes with itself due to wave-particle duality (existing as a probabilistic wave before being measured but as a particle once measured).
10. I thought matter is destroyed when it is converted into energy?
14. The topology of the universe depends on the intrinsic background pressure of space and we haven't yet been able to ascertain whether it is slightly positive, slightly negative or perfectly balanced...
15. I thought was a trick question as nothing with mass can be accelerated to light speed. Photons are the only particle known to move at light speed and they have no mass.
You may well know that I'm wrong about all of these, especially as you've made a quiz about it, in which case sorry for doubting!
4. You are essentially correct. I wasn't thinking of the double-slit experiment when I wrote the question, but that works. I've added an addition explanation which may clear things up.
10. That's true. I will change the wording of the question to be more accurate.
14. I was relying on the inflationary theory, which I believe is widely accepted (could be wrong). This theory does confirm that the Universe is flat.
15. You are also correct, I will change the wording of this question
That might only occur with virtual particles though, I'm not sure.
Also, Q. 16 is more in the field of epistemology / metaphysics than quantum mechanics
I enjoyed the quiz though :-)
Anyway, as for those questions...
7 : I don't agree. A singularity is not part of spacetime.
8 : Nope, light always moves at the speed of light. What "slows it down" is the numerous interactions with the particles of the material it crosses (which also cause scattering). So you're just talking about the effective speed of light in a given material, not its true speed.
12 : No, antimatter is affected by gravity in the same way as matter. Mass as no sign, it's purely attractive (at least for timelike particles...).
14 : It depends on what you call a shape, but the universe is definitely not flat, that's all the point of general relativity...
15 : Mass is a constant. I don't like the interpretation where particles are said to have a higher mass at higher speed. Call it rest mass if you want, but it's the only value that has an interest. It's better to say that E= mγ(v) c².
(Too bad I can't edit my previous comments anymore ;) )
4. Electrons, along with any particle, can exist as a wave. However, that is not the same as existing in multiple places as once.
7. It is unknown whether the singularity at the center of black holes truly is infinitely dense.
8. When light is being refracted through matter, it is being absorbed and re-emitted by the matter. This "slows" the light down by creating a large path.
9. Protons can absorb an electron and anti-neutrino to form a neutron.
11. The Many Worlds Interpretation does not discuss consciousness. This is a pseudo-scientific thought experiment of quantum mechanics known as quantum immortality.