These things are plot necessities, but they aren't plot oversights.
Why doesn't Starfleet ask the Ba'ku pretty please, can we have eternal youth? Because the Son'a tell them the Ba'ku cannot be communicated with - they are primitives whose society would crash and burn if Starfleet as much as said "We come in peace". (Which shouldn't fool Starfleet for a split second, because a single native village of half a thousand people could never have attained the iron age technology witnessed. But perhaps the Son'a had ways to make Starfleet believe that these were the last survivors of a more widespread, truly native culture. The Ba'ku probably aren't your typical n'th generation survivors of a starship crash, either, so Starfleet would give the native theory the benefit of doubt.)
Why don't the Ba'ku ask Starfleet pretty please, can you go away if we give you eternal youth? There's no grounds for dialogue when the spying plot is first revealed; too much distrust around. There's no trust in Picard even after he turns out to be a fairly decent guy, because the Ba'ku have nothing to gain from revealing they remain forever young - it's a secret they desperately want to keep, and they don't know the aliens are already after the very thing. (Okay, they did hold a few Son'a prisoner for a while, so they do know who their real enemies are. But that's not something they would wish to discuss with outsiders who are in obvious cahoots with the Son'a.)
And then the holoship abduction scheme is revealed, and Picard beams up right away to strangle Dougherty - so there's no time to talk peace with either of the Starfleet stiffs. And then the guns start to do the talking.
The writers went to a lot of trouble to make it plausible that the truth cannot be revealed. It all becomes necessary not just because the drama calls for it, but because the events do.
As for evacuating the kids, that would make no sense. Why not evacuate the entire population? They aren't going to score any actual points by staying. But Picard wants them to make a symbolic stand, and those are far more effective with cute kids than without.
sorry, but there are various points where they could have been asked. That part where Picard beams down alone and asks the Baku how old they are, and then right after the conversation with Dougherty. Why doesn't EITHER of them suggest during the conversation, that now that contact has been made with the Baku already, that they should just go ahead and attempt to negotiate?
Why don't they? Because it's classic plot-necessitated stupidity. It's like those sitcom plots where there's a huge misunderstanding that would really be resolved with a five-minute conversation. Picard, a diplomat by instinct and nature, DOESN'T suggest doing this because as T'Girl
points out, there's no way it could end well. To have a movie, they have to say no.