If I poisoned my fire enchanted sword with 50% weakness to fire and struck a bandit would subsequent strikes cause MORE fire damage?

And does weakness to fire poisons work on undead such as draugr and dragon priests? I keep hearing/reading mixed opinions on this.

The WTF poison would not effect the applied strike, but all of the subsequent strikes would. That is...until the poison timed out.

Dragur are immune to poison. Only "flesh" NPCs are effected by poison.