Hmmm.
1. Either is correct, but elapsed is a much more posh and educated way of saying "went by". When in doubt use longer, fewer words to impress the psuedo-intellectuals.
2. Wrapped up means simply wrapped, and bound up means restrained or tied down in some way.
3. Again, both are correct, but approached is better as a longer word in place of two short ones.
4. I would say I walked "up" to her, and I would use "reverance" instead of "veneration" - I think it's just more common, but means the same thing. I could be wrong though, as I don't use either of those words often.
5. If she is injured, you should say "groaned". Sighing and moaning infer something else.
6. Is gaffer British? I've never heard it used before outside of LOTR.
7. Haggered describes a whole person, not their eyes. Haggared and overstrained are also not really synonyms. Haggared means that someone is tired, or worn out, a mess, stressed out, about to collapse, etc. Overstrained (for eyes) just means that you've been staring at your computer too long and probably inflicted permanent damage on them and need to see a doctor. It's acceptable to say that your eyes are "tired", though.
8. All are correct, but postpone is one longer word replacing two shorter ones in both other cases, so I pick that.
9. Both are correct - I don't think one is more proper or common than the other though.