Does Edge of Tomorrow have an open ending?

The ending was supposed to be this vague. In an interview with Christopher McQuarrie he says:

“I was always arguing it has to end on the helicopter,” he explained. “You have to be thrown back to wondering, ‘Did the movie even happen? Did any of this really happen?’ To that end, there were a million things you had to do with the writing and visually, to serve that ending. That presented a lot of challenges and debate for us. We really struggled to deliver what the movie needed to be emotionally. I know the ending was somewhat controversial, with some people who didn’t like it. I think the only way to make those people happy would to end the movie in a way that wasn’t happy. We weren’t interested in doing that. It needed to end in a way that wasn’t harsh.”

Therefore, ending was supposed to be an open ending that makes the audience wonder whether the events actually happened. In which, for me, they succeeded.

Yes, I'd say so. I don't think there's any clear evidence regarding the Omega's status (or the Mimics in general) - at least not within the movie.

I'd also like to refer to my answer on this question regarding different reset points:

How about this theory? I think it's a bit different to and might be hard to understand, based on how we perceive the story as a linear movie:

After watching the movie, I still wondered how one or more entities would be able to somehow alter time in the whole universe to create the resets. A bit like The Butterfly Effect? Nah, didn't really make any sense to me.

But then I've had the idea to understand the resets in a different way:

The Mimics aren't able to time travel or reset time in any way. However, they're able to somehow transfer knowledge/memories back in time utilizing something in their blood.

While watching the movie, we always notice Cage waking up, obviously shocked by the death he experienced just moments ago. But what if he just got that memory that very moment (or just before) similar to how dreaming works.

[...]

So the only question this doesn't answer: Why is the Omega gone after the last "jump cut"? Did it retreat or hide, since it knew the humans now possess the knowledge of how their "mind trick" works (even if it's just speculation)?

And that's exactly the point in your question. Unless there's some more information in some source outside the movie, I don't think there's any clear answer (and still the possibility for a sequel?).

Also, let's just assume we're indeed talking about time travelling (not just transferring knowledge), why should the Omega be gone? It died in the future, it's not like it dies in the past as well (unless there's some connection that didn't get mentioned). As such the possibility of a retreat or hiding somehwere would be the most logical conclusion to me.

After Cage became an Alpha and entered the nervous system of the Omega, could it be the Omega that revives the Human-Alpha and not himself, to lure him in a trap by sending him visions ?

Carter said that Cage had the power, but I'm not sure of this. He never seemed to control it and I know it doesn't mean he didn't have it but maybe the Omega still had the power and wanted to make him believe he had it to kill Cage in a trap. Besides, when the Squad J is in the plane to Paris, Griff said that Cage told them not to kill an Alpha because the Omega would replay the day and all would be lost. Wasn't Cage supposed to have stolen the power from the Omega ? meaning that it couldn't still have this power. If he never had and controlled it, why the Omega didn't just replay the day on its own, like it did each time the UDF won a battle ? I'm not sure it needs the death of an Alpha to reboot, because it would mean that humans have killed Alphas in almost every battle lost by Humanity and that the Omega would have replay all these days to win. It seems very incoherent to me. Or I really don't understand a single thing in this.

Anyway, I think Cage never had the power. After many deaths and a good knowledge of his enemies given by the Omega (which was replaying the day all over), Cage was now trained and capable to survive long enough. It let him reach the point it wanted (for Cage, the dam, for Rita, Verdun) and made him believe it was there to kill him slowly.

For Rita, it was slightly different as the Omega wanted the Humans to win the battle but probably didn't expect her to kill an Alpha and enter its nervous system. Then it pulled her to a place around Verdun with false visions where Alphas could kill her. The Omega sort of trained her to win the Battle of Verdun and then to come in the trap but she finally lost her ability during the fight and was no more a threat to it. Then its plan continue with the Operation Downfall.

In the end, the Omega is dead, and can't revive by time travelling since its blood melt with Cage's like did the blood of the first Alpha... which never reappeared on the beach. How to explain the final time loop ? it could possibly just be the deep and unconscious willing of Cage with his new power. Anyway, the Mimics and the Alphas are already dead before the Operation Downfall since the Omega is no more. Rita is alive and Cage will tell her in details how the Squad J and her helped him to kill the Omega. The happy ending is not so bad.

I don't think the Omega was intelligent. Instead, I simply think of it as a machine. The Alpha's are the one controlling it, as long as they hold the key. It would make sense if the Omega had created some time region that got reset when it was killed - by why would that reset only a few days back, instead of to the beginning of the invasion? Did it create a save point after Verdun? :D

And of course, why would this reset result in a world where the Mimics are all dead? IMO it would make a lot more sense if the Mimics were still there to fight, just without their major advantage - or maybe even flee back home, having lost their strongest weapon.

In the end, this was probably added to the movie just to make the ending "good" for western audiences. If this was a Japanese movie, it'd probably end with everyone dying, but ultimately achieving their goal. It's just that noble sacrifices aren't really what european-descent cultures really appreciate all that much, when it still leaves the hero and all of those he loved dead :D

Note that in the story the movie is based on,

the final reset doesn't happen, and Cage (Keiji Kiriya) kills Rita in the end.