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Take a look here and here for information on Business Property Relief which is what protects shares in certain trading companies from Inheritance Tax. There is commentary here.
1 There isn't a list of AIM companies which qualify for BPR and, therefore relief from IHT, as a company can move between being a qualifying company and being a non-qualifying company depending on what its business activities are at any point in time or it is being sold or wound up. Investors have to do their own due diligence and maintain a watch on such companies. The company you have shares in may be able to give you its opinion on whether it currently qualifies for IHT relief or not. There are investment vehicles which invest in AIM companies and they will monitor eligibility for IHT relief.
2 If your executors consider that your Sirius Mining investment qualifies for IHT relief, they will make the claim for the relief in their submissions to HMRC (IHT400) following your demise. You don't need to do anything now yourself but try to find out if the company qualifies based on HMRC rules.
I hope this helps but let me know if you have any further questions.