Only the base weapon is required; no upgrades or progress along the Arms of Balrahn questline is required.
The weapon must be equipped in your main hand to activate the cutscene.
If you choose the wrong answer (saying something like "He has shifty eyes..."; this implies you don't trust him) he will get very angry and you will not start the quest. Zone out and come back again for another chance.
Once you have acquired enough Weapon Skill points, you will see Drakesbane available under your list of weapon skills, but only while your Radiant Lance is still equipped. There will be no message in the chat log informing you of this; it will simply appear in the list.
If you want to check your progress, return to Zalsuhm and trade the weapon. The messages he gives you indicate your progress toward unlocking the Weapon Skill:
"The energy is threatening to burst forth. It won't be long now, hee hee hee..."
You accumulated all Weapon Skill Points and can see the weapon skill in your menu when you have the Nyzul weapon equipped:
"You've done it! Energy is overflowing as though the floodgates have burst open!"
This message only appears after the unlocking is complete, and is followed immediately by unlocking the weapon skill completely.
Weapon Skill Point Requirements
Your current number of completed floors is used to determine how many points are needed. For example, if you received the weapon and started the quest with 90 floors completed, and then did a 91-95 run, you only need 580 points to unlock the Weapon Skill. If you already did 580 points with the weapon, you will get the weapon skill when the progress is saved to your Runic Disc.
In other words, continuing to record higher floors on your Runic Disc cuts down the required amount of Weapon Skill Points needed even if the quest is already active.
Self-styled leading researcher of mystical artifacts, Zalsuhm, claims that the weapon you acquired deep within Nyzul Isle conceals immense power. Wielding the now unlocked weapon will cause a magical evolution to take place...eventually.