If a target is inflicted with Hexblade's Curse, would hitting that target using spell attack (for example Scorching Ray) trigger the additional damage? and if so, would it affect each "ray" with additional damage?
Yes, it does.
You gain a bonus to damage rolls against the cursed target. The bonus equals your proficiency bonus.
So long as you roll for damage you get the bonus. The bonus applies to each damage roll, so if you roll damage multiple times for a spell (e.g. scorching ray), the damage bonus applies to each roll.
Yes, it does. But only once per spell, or per attack roll.
In this case, you deal the damage of the weapon or spell and (according to PHB 196, "Damage Rolls") you can then add your proficiency bonus.
In the case of spells that require multiple attack rolls, congrats - you get the bonus per attack.
In the case of spells without an attack roll, sorry you just get to add the bonus once.