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When it says you can choose any of certain named characters(Sicarious, Shrike, Vulkan etc) to choose as a Captain in a Formation, like the Demi Company, is it legal to pick another SM army's character? I'd assume if so the Chapter Tactics not mixing rule kicks in, but otherwise, are there any other restrictions?

You can pick from the characters listed; it really is not any more complicated than that. As far as I know, all units in a formation must be drawn from the same Chapter unless specified otherwise.

From 'Chapter Tactics' in Codex Space Marines:

All models in the same Detachment or Formation must be drawn from the same Chapter.

So the answer is no, what you're asking is not legal.