A lot of modern health woes are turning out to be caused by inflammation, and HCQ is a relatively safe, cheap immunosuppressant. It makes sense that it would help out. As far as conspiracy theories go, it's been profitable for various parties to suppress knowledge of it over the years, as they can't patent it then sell it for extreme markup. I myself take a $10k/month immunosuppressant to treat a condition that HCQ is also effective for.

No, it's available in generic form.

No. Interestingly, the root cause of all these positive correlations might be the same. One thing that Hydroxychloroquine is undeniably good at is that it's a very effective dewormer. Anything that is either caused or made worse by worms, or by the immune system going haywire because of worms, will be improved by Hydroxychloroquine.

So, it helped against covid (in key populations) because one of the key interventions against covid will kill you if you also have worms. So in places like Bangladesh and Pakistan where intestinal worm infections are common, covid outcomes improve because the worms got killed. If this[0] is correct (and it is a very new result, so might as well not be), the positive correlation might well be that your immune system stays calmer if you have no worms.

[0]: https://www.cell.com/cell/fulltext/S0092-8674(22)01463-5