Can the Omega in "Edge of Tommorow" be killed?

There is a point in the movie where Emily Blunt's character, Rita, speculates that Humans may be the first species to be able to effectively fight back against this alien, because of how we can absorb the time traveling ability when exposed to their blood.

Both Rita and Cage are, at different points in time, exposed to the blood of an alpha, and gain the ability to reset time by one day. Both later lose this ability due to a blood transfusion.

Near the end of the movie, Cage manages to kill the Omega, but in doing so, receives mortal wounds himself. As his dying body floats in the water, it is exposed to the blood of the Omega. The Omega, being more powerful than an alpha, it's blood gives Cage greater power to reset time, and so when his body dies, it resets time several days back, to the point before Cage meets General Brigham.

Now the viewer is never shown how or why, but somehow the Omega's death in the future ripples back in time, killing it in the new present. Because the aliens have some kind of group consciousness, the death of the Omega causes the deaths of all the aliens. Earth is saved and only Cage knows why. Although if he explained it to Rita, she would understand and believe him because of her previous experience with the alpha and knowledge of the Omega.

It is made clear in the light novels, only signals, like brain waves, can go back in time. When and what gets sent back is normally controlled by the Omega. It seems as long as Cage has control over when a signal is sent back, the Omega does not.

Therefore, what you witness in the movie is basically a loop in consciousness experienced by Cage, which happens within a single loop of consciousness being experienced by the Omega. Cage's loop will only stop when his signal stops getting sent back in time, either when he manages to destroy the Omega, or if he loses the power, and it reverts to the Omega which then takes back control of the loop.

When Cage killed the Omega in his last loop, he apparently regained the power to send his consciousness back, taking it from the Omega like before. The Omega thus did not end up sending back information to its past self as it died, and so the Omega's loop of consciousness was finally broken.

I think it is then implied that the Omega in the now present dies as a result of its broken loop of consciousness.

How do you teleport yourself back in time after you've been killed? The omega was able to send alphas back in time, after their death, because the omega still existed. The entire point of the movie is that killing the omega removes this ability from the aliens.