How long were the clones on Earth?
While debatable, the clones where first deployed between 2017 and 2027. My personal guess goes to the latter. We know the current year is 2077 and the war started 50 years ago (mentioned in the introduction). We also know the last Super Bowl occurred in 2017, and can assume earth civilization was interrupted thereafter. We also know the Odyssey reached Saturn in 2017 (flight recorder). I postulate that shortly thereafter, via some advanced propulsion, the Tet reached Earth and destroyed the moon. After a 10 year hiatus (2027), the clones were deployed to annihilate any remaining organized resistance.
How long were the particular couple manning tower 49?
Let's start by ruling out possibilities. The clones age naturally, and from the flashback scenes to the Odyssey mission do not appear noticeably older. Their memories had been wiped approximately five years prior. This we assume to be either an irreducible side-effect of the cloning, or a required form of indoctrination. In either case, there is no guarantee that any individual clone is limited to a five-year service period. We also know that while there are a considerable quantity of clones in cold-storage aboard the Tet, there are certainly not enough to constitute an army. Assuming that indoctrination is not required, Occam's Razor suggests that it would be simpler to discard each pair after a five-year stint rather than invest in mind-wiping techniques. While it is possible that each team is employed for simply a matter of weeks and memories for the previous five years of the assignment fabricated, reasoning along similar lines shows it to be highly spurious. The alien presence would obtain no discernible advantage, and furthermore there is reason to suggest it does not in fact possess the capability to implant memories. It would be reasonable to assume mind-wiping is a much less advanced procedure than memory manipulation. In fact current electroconvulsive therapy (ECT) is able to destroy memory, whereas memory manipulation remains firmly science-fiction. It would also be reasonable to assume that memory implantation implies memory-extraction, and throughout the film the only proof Vika and Jack have of their outside existence could easily have been obtained by scouring the physical remains of the Odyssey command capsule. Why would the Tet employ such subterfuge with only a romantic picture and the voice of an obscure "Sally" as evidence if it could manipulate memories to such a fine degree?
What would have happened after the final two weeks concluded the five-year stint?
XKCD goes into quite an involved What-If ... Drain the Oceans. In short, it would require thousands of years to drain the oceans. The density of hydro-rigs, the vast expanses of water pictured throughout the film, and simple geography (Chicago bedrock, limited plate movement, flat land, Empire state building below ground level), suggest the Tet was nowhere near even making a dent in the Earth's water supply.
Nonetheless, as mentioned above, Jack and Vika would clearly have returned to the Tet for either indoctrination or recycling - destruction and replacement with another clone pair.
So what was the Tet actually doing. Would it have been finished in two weeks?
We have no way of knowing. Malcolm Beach quotes, "What a brilliant machine. Feeding of one planet after another for energy.", but there is no way to ascertain the veracity of this quote. Quite possibly it would have stayed with the Earth until all its natural resources had been depleted, its host "killed". Seemingly the Tet is only interested in energy - possibly being able to synthesize matter from energy - and at its level of technology I assume it could more easily obtain energy from suns rather than planets. Yet if the Earth was simply a gas-station, a recharge point between two interstellar hops, why focus specifically on it? Europa, Ganymede and Callisto also contain copious amounts of water, and would be nearer Titan than Earth. The Oort cloud is theorized to be five times more massive than the Earth in aggregate, and to be composed mainly of ice. Possibly the Tet was sent specifically to terraform Titan, with the mandate to destroy any interfering life-forms. It may have viewed the "war" as simply a territorial dispute, and contact with Odyssey as the unfortunate spark. On the other hand, the Tet may have been a rogue machine gone psychopathic, roaming the galaxy from planet to planet with the sole purpose of exterminating organic life. Its final words, "I am your god", may suggest a megalomaniacal ego, or could simply have been a final attempt to stay its execution through the application of reason (versus emotion).