Maybe they will do a new one every month or two. There's several unreleased Mythicals to work though. I hope they move Shiny Mewtwo to Special Research too. He's been an EX boss long enough
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Is it confirmed that we can only catch one Mew?
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For now yes. They could recycle the quest at later time though if they wanted, or even make Mew a raid boss at some point in the future after everybody has one. I kinda like it being a one time thing though. I wouldn't mind if Legendaries were limited to one either, tbh
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I just finished up the questline today, and this is what appears under the special research tab after catching Mew. So for now, that's all she wrote, but it looks like there's definitely more coming in the future.