1.) Should Double Jeopardy be eliminated? Why or why not?No, I don't think it should be eliminated. It is a powerful protection against the potential that a state will try to persecute an individual within the law. (As opposed to just "disappearing" people.) In most modern socieities, I think that if we got rid of double jeopardy, it would be less likely to be abused by central government, than by local police and prosecution authorities trying desperately to put people away that they "know" are guilty, regardless of the evidence available.
2.) Who does it benefit more, the individual or the government? Why?The Individual is vastly better off with double jeopardy in place.
3.) What could be done to revise the current Double Jeopardy system, if anything? What and why?The main drawback I see with double jeopardy is the uncovering of new evidence after the trial has completed. This has been of particular concern in the last 5 or 10 years, since the advent of reliable DNA identification.
Many "guilty" people have been later found to have been wrongly convicted on the strength of such evidence, and have been set free and compensated. Rightly so (in murder cases, this alone is convincing enough reason for me to oppose capital punishment, but that's another thread

).
Intuitively, in a justice system that (again, rightly) places more the burden of proof on the prosecution side, however many innocents are imprisoned will be at least equalled by guilty men that go free because the evidence did not convince a jury beyond reasonable doubt at the original trial. Because of double jeopardy, such men (or women, but let's be honest it's mostly men) cannot be retried.
To that end, the only thing I would like to see changed in the justice system is to adopt the additional "not proven" verdict that is in place in Scottish law. Anyone found "not guilty" is protected under double jeopardy, as now. Anyone found "guilty" has the same rights of appeal and retrial (in the face of new evidence) as they have now.
But a jury can choose to decide that a case is "not proven". I'm not expert in Scottish law, but generally they do this when they think that the defendant is guilty on the balance of probability (as in civil cases) but not beyond reasonable doubt as the criminal law requires. In such cases, the defendant is released but not exonerated, and they can be retried should new evidence come to light later.
So it is not in the state's power to choose to persecute someone - only the jury can decide if further suspicion is warranted.
So I quite like the idea of a tripartite jury decision.
I'm sure it has it's own weaknesses, but overall it seems more satisfying thatn either removing double jeopardy, or the current system as is.
4.) Should there be any exceptions to Double Jeopardy? If so: in what case and why?Only to the extent I've outlined above.
5.) Is Double Jeopardy still useful or is it outdated?It's very useful and not outdated at all, IMO. It has weaknesses, but I think adding "not proven" to jury outcomes ameliorates them.