hello,
can i use "precise strike"'s first ability when i attack with "dancing weapon"?

Yes, Precise Strike only looks at the weapon's type, not the attack type.

(forgive the size)

preform a "Ranged" attack with a melee weapon. when you declare and attack with a melee weapon, blahblahblah, you get the idea. the only thing it costs the hero is the extra strain and the action.