Zero-confirmation double-spending is a small problem, and possible solutions are known. (E.g. trusted third party + multi-sig addresses for small-value transactions.)
On the other hand, protocol changes like described above might have game-theoretical implications which are non-trivial and hard to understand.
The above approach works as long as the majority of hashpower is honest, defined to mean, working to stop double spending. This is the same security property as described in the white paper, thus this introduces no new security assumptions.
No. Bitcoin should work if miners are merely individually rational, i.e. they try to maximize their pay-offs without colluding with others.
I guess word "honest" might have different meanings, that can be a source of confusing.
1. Honest -- not trying to destroy bitcoin
2. Honest -- following rules which are not required by the protocol