It would have to, unless you also consciously increase the rate of evaporation at the same time. Could be bad news for countries with arid neighbors to their direct west.
I don’t think it can be assumed. if the rain increased vegetation, i wouldn’t rule out an increased water cycle and greater amount of water in the area in general. Honestly, i wouldn’t be surprised if it benefited neighbors. I’m no expert and there are countless variables, maybe a high percentage of the rain used then sent right into the ground as waste water- never to have the chance to evaporate. or never taken up by vegetation at all. Time reveals all, despite whether this was a hasty experiment.
True, while it will certainly remove moisture from the air that would necessarily have fallen elsewhere, it's difficult to say whether or not it would cause measurable decreases in rainfall in places that would notice it. For example, we know that reforestation actually increases precipitation downwind, as trees draw water out of the Earth, which then evaporates out of their leaves. However, a nation that's seeding clouds isn't going to be doing it because they're trying to create rainforests, they'll be doing it because they want agriculture and clean drinking water, and it's unclear whether or not that can possibly give more than it takes from downwind neighbors.
Sounds a bit like the dispute between Ethiopia and Egypt over Nile Water (Ethiopia is building a dam) so definitely plenty of political precedent for conflict over water resources and this will exacerbate this.
Possible but a lot of rain just falls in the middle of the ocean, so not a great loss.
If that moisture they're making fall out of the sky is guaranteed to end up falling above the ocean otherwise then sure. Otherwise you'll get conflict.
Which will now wash a load of filth from the land into the ocean instead.
the moisture has to come from somewhere, nothin is free