However, somehow (totally inexplicably) Alex knew Helena was pregnant
He knew because his friend Xiao told him. They found out that Helena was pregnant, along with the fact that she could not survive in the outside world,when Alex brought her to his clinic to run some tests on her. That's why Xiao told Alex "There's something more" (~1h21m).
The ending is rushed and poorly explained, but after watching it a couple of times I think it's clear that Helena's "one condition" was not only to give their daughter freedom (not once she reached a specific age), but also that she would be one of the settlers to leave Earth and travel to Celeste when the project was ready to go. Hugo mentioned that "with a little luck we'll see the first ships take off in 20 or 30 years" (~22m). The news on the radio even reported that the first ships to Celeste could be launched in 15 years (~30m) The daughter looks like she's around that age and we also see an older Hugo meet her outside the simulator. As hinted by the background "launch countdown" voice when she is exiting the simulator, they came to take her to one of those ships.
Regarding Helena and Alex, the daughter briefly looks back in the end and we can see the shape of a person at the entrance of the simulator. That person is not clearly shown but it had to be one of the parents, probably her mother since Alex had some kind of sickness (he could be dead by then) and Helena was a genetically-exact copy of a very healthy and long-lived person (~1h03m). Maybe both were there, but as I said only one person is shown.
It's not a bad movie, but I don't really understand why they had to make a "poetic", almost open end instead of clearly explaining it, as they had been doing with everything all along the movie. It's a bit confusing and I can understand why people could be frustrated with the rushed ending being squeezed in less than two minutes (and be left with that "what the hell did just happen?" feeling).
Thank you Devotee, it sounds like your multiple viewings turned up some interesting observations. The only thing that had me mystified was the final shot of everyone being there as the daughter walked outside (and just what was going on there), but it does sound very possible she could be one of the first people travelling to Celeste (for real), and so they were celebrating her "graduation" of sorts, and the transition to a new stage of her life, just as you say. I suppose another thing I wondered about was how she would live outside the simulation (since Helena couldn't survive for long that way), but maybe she was allowed to leave the simulation regularly to acclimate to the real world... except then you'd think the data that one guy wanted to collect would be skewed (unless she had to stay inside until she was 4 or something like that). So yeah...
I suppose another thing I wondered about was how she would live outside the simulation (since Helena couldn't survive for long that way)
My guess is that she never left the simulator until the moment shown at the end of the movie. She doesn't need to acclimate to the real world since she is not going to live there, it's very likely that she's immediately transported from the simulator to a real ship to Celeste, both sharing the same environment conditions.
Now that sounds like a satisfying solution. Thank you.