Problems 1 through 14 were worth 7 points each and problem 15 was worth 2 points.

1. Although the terms "dark matter" and "dark energy" are just placeholders, their effects have been quantified (measured). Those other three things were never seriously quantitatively described.
2. Its speed is constant in a vacuum, and more importantly, its speed is the same relative to all observers (in the right kind of frames, at least).
3. Hume probably wouldn't have changed his philosophy much if at all. Although we don't normally "experience" the effects of relativity through our senses because we can't travel fast enough, Empiricism simply asserts that knowledge comes through sensory experience as opposed to intuition, revelation, or guessing. Since we can directly observe (and sense) gravitational lensing, the perturbation of Mercury's orbit, and the workings of GPS, relativity remains consistent with empiricism.
4. Because it is itself inductive.
5. It's deductive as can be, a perfect example of Modus Ponens. However, we cannot conclude the conclusion is true unless the premises are shown to be true, and there is no good reason to believe they are.
6. B_jB_rB_j∀p.Cp⊃◊F(Rc∨Lc)
7. If the set of all possible xs is infinite, you certainly cannot look at every single x and show P is false for it. What you can do, though, if you believe in classical logic, is show how the negation of this statement would lead to a contradiction. The negation of ∀x.~Px is ~∃x.Px. Now if you can show that a contradiction would arise unless some object existed with property P, you have proved the desired negative universal.
8. P(D|y) = P(y|D)P(D)/P(y) = P(y|D)P(D)/(P(y|D)P(D)+P(y|~D)P(~D)) = .95(.0001)/(.95(.0001)+.05(.9999)) = 0.001896586, or 0.1897%.
9. Assuming the nose grows only in response to a lie, then one can't make the statement true or false without a contradiction. As for causing trouble for the genie, say "I WISH THIS WISH WILL NOT BE GRANTED."
10. "Teacher strikes idle kids" is ambiguous because of these two parse trees:

                 S                                S
              /     \                           /   \
           NP         VP                      NP      VP
         /    \      /   \                  /       /    \
       A        N    V   NP                N       V       NP
       |        |    |    |                |       |      /  \
       |        |    |    N                |       |     A    N
       |        |    |    |                |       |     |    |
    Teacher strikes idle kids           Teacher strikes idle kids
    

    "I saw the girl on the hill with the telescope" also has multiple parse trees. Here are two, but there are more:

             S
          /     \
       NP          VP
     /         / / | \
    N      /-/ /   |  \---------\
    |    /    /     |             \
    |  V     NP     PP             PP
    |  |    / \     / \           /  \
    |  |   D   N   P    NP      P      NP
    |  |   |   |   |    / \     |     /   \
    |  |   |   |   |   D   N    |    D     N
    |  |   |   |   |   |   |    |    |     |
    I saw the girl on the hill with the telescope
    
         S
       /   \
    NP       VP
    |    /   |     \
    |  V     NP       PP
    |  |    / \      /  \
    |  |   D   N   P      NP
    |  |   |   |   |    / |  \
    |  |   |   |   |  D   N   PP
    |  |   |   |   |  |   |    | \
    |  |   |   |   |  |   |    P    NP
    |  |   |   |   |  |   |    |    |  \
    |  |   |   |   |  |   |    |    D    N
    |  |   |   |   |  |   |    |    |    |
    I saw the girl on the hill with the telescope
    

11. If the starting point is 1, the sequence immediately converges to 1. If it starts at 1.000000000000001 it diverges to ∞. It is not chaotic because the orbit is not dense.
12. Your examples of beauty and awe are your own of course, and almost anything counts. The second part of the question does have a definitive answer, however: Many nonscientifically literate people confuse beauty with mystery. And while mysteries can be beautiful, nonmysterious things can even be more beautiful, because knowledge of the structures, processes, and quantity behind many phenomena give the scientifically literate observer so much more to contemplate and feel awed by.
13. One can make decisions without being consciously aware that the decision was made. The fallacy held by those that say these studies disprove free will is that of conflating consciousness with the agency that make the choices. Society of mind, people.
14. You can say that Severus Snape is either real or not real, depending on whether you take the name to denote (1) the idea of the character or (2) a (flesh-and-blood) human occupying our timeline here on earth. "Severus Snape" is a real two-word phrase, a mention. The third item is a stylized piece of language, and therefore counts as a mention and is therefore real.
15. Answers vary.