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Can a Warperson suffering from one (or both) of these conditions allocate/leech focus/fury normally?

Yes. The act of shaking comes during the same phase as focus allocation, which is before the models activation.

This would also be when jacks/beasts shake effects too. One of the focus allocated to the jack is used to shake the effect, or the beast is forced to shake it.

If you check on p63 of the rule book, under "Knock Down" there's a precise list of what a knocked down model can't do. While a knocked down warcaster cannot feat or cast spells while he is knocked down, there is nothing stopping him from gaining or allocating focus as normal (or in the case of knocked down warjacks, being allocated focus), so that's fully allowed.

Hope that helps

I certainly does.