I believe this is relevant too: https://www.loomio.org/d/R3zBvnfc/improving-and-expanding-hashtags-usability
I think implementing this is a really important feature, both in search and in the left-hand menu (i.e. what you call preset streams).
Some further thoughts:
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In search, all the parameters you list could be useful.
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In the left-hand menu, I think all one needs is the ability to combine hashtags together (i.e. to follow posts with #france AND #politics), and the ability to combine users with hashtags (i.e. follow posts from @Jakob on #Denmark).
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Currently, clicking on the “followed tags” label feels like being taken to a new stream, and clicking on one of your followed tags feels like being taken further to a new stream. It would be great – as you suggest – if when one clicks on them, they feel more like a filter on the stream than a link to a new substream. And (as in the previous bullet point) if one could have several selected at once – so although I follow 20 tags I could get the stream to display only posts with tags #football, #vegetables, #coffee and then decide I also want to hear about #bread, but not about #football, so deselect the latter and select the former and the stream automatically reflects that. (and so on for aspects…)
Diaspora’s functionality would be (even more) incredible if you could do these things.