Soul-Scar Mage and Nin, the Pain Artist with lifelink
Your assumptions/guesses are all correct.
A replacement event completely replaces the thing it replaces with something different.
In this case, Soul-Scar Mage replaces the damage produced by Nin with -1/-1 counters.  Because Nin is no longer damaging something, lifelink from the Basilisk Collar doesn't happen.
The opponent still draws X cards, because the X is tied to the mana spent to activate the ability, not to the amount of damage dealt to the creature.