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A keen weapon doesn't double the damage, but doubles the threat range. For example, a scythe hits critical damage on a roll of 20. A keen scythe hits criticals on rolls of 19 and 20 (i.e. doubled). Improved critical doubles the threat range again, so the scythe would now hit criticals on rolls between 17 and 20.
Another example, a raper criticals on 18-20. Improved critical or a keen rapier makes this 15-20 and finally, improved critical with a keen rapier makes it 13-20.
Sorry not sure about the domains.
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