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I think this is way too much functionality for an Obsidian plugin. But one possibility would be to use another program like Instaloader to download the Instagram data. I think that it is not possible to download your feed, but only individual accounts, storys and posts. But I tried Instaloader a few weeks ago and it wasn’t working for me.
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What do you mean by “fetch instagram urls”? Do you want to show only certain instaram URL’s in your Daily Notes? You could do that with automated templates. To do this, you create a template for your Daily Notes and then have it automatically inserted as soon as you open Obsidian.