Neither the backend nor the UI appear to treat #this specially; it's just a piece of text.
A line beginning with # (with a space) is treated as a headline:
this post was submitted on 07 Jul 2023
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Lemmy
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Oh good, I love Markdown.
None so far.
In the end they have a similar role on Mastodon etc. to what communities do on Lemmy, so there is not that much point in replicating that feature on Lemmy.
So, it's more of a mastodon thing, but if you post to lemmy from mastodon, with a hashtag in the post, it will be rendered here as a link to a mastodon feed for that hashtag. I'm guessing that's done on the mastodon end though.
AFAIK no and yes that should be a local Mastodon thing.