These are obviously old questions and all the answers are also old. Things have changed quite dramatically over the past 4 years. The Instagram API has never offered to publish content and never will. In fact, the Instagram API is currently on the way out. Just go to https://www.instagram.com/developer/ and you will receive a notification about this.
At the beginning of 2018, the Facebook Graph API began offering images on Instagram, but you need to convert your Instagram profile into a business profile, which just means connecting it to your Facebook page. At the end of 2018, video support was added to Facebook.
Bottom line - today it is absolutely possible to publish videos and images on Instagram: https://developers.facebook.com/docs/instagram-api/content-publishing
Caution - you cannot easily access this feature. It is available for select applications only. You can try to become a Facebook partner: https://www.facebook.com/business/marketing-partners/become-a-partner - although this is a lengthy process.
While you are working on this, feel free to check out our Instagram posting API: https://concretesocial.io (yes, I'm one of the authors).
Chris bovan
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