1. Takes -5 to each attack roll and adds +10 damage to each hit creature.
From the part of Sharpshooter (PHB, p. 170) that you've included (but with different emphasis):
Before you make an attack with a ranged weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack's damage.
This applies to "an attack with a ranged weapon"1, not the Attack action. See What does upper-case-A-Attack action vs. lower-case-a-attack mean? for more on the difference between "the Attack action" and "an attack".
Reading the Hunter Ranger's Multiattack feature (PHB, p. 93):
You can use your action to make a ranged attack against any number of creatures within 10 feet of a point you can see within your weapon’s range. You must have ammunition for each target, as normal, and you make a separate attack roll for each target.
This describes "a[n] ... attack", so Sharpshooter could apply to each attack roll (or not2). You take the Multiattack action (not the Attack action), which involves many attack rolls, each of which could be used in conjunction with Sharpshooter.
This reasoning is based on the generic advice given in the PHB (p. 194):
If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.
1 The definition of "an attack" with regards to a Hunter Ranger's multiattack is confusing. In this Q&A, it seems that Sage Advice has said that Multiattack is one attack with many attack rolls. But then if that's the case, it raises the question asked; when does Sharpshooter apply then? Hence in this case, I've drawn attention to the fact that Sharpshooter is specifying "an attack with a ranged weapon", which I take to mean one of the attack rolls within the Multiattack "attack". From this I conclude that Sharpshooter applies to each attack roll, not just the Multiattack action.
2 To extend this answer to take into consideration the extra question, there's nothing about the text of Sharpshooter that implies that it must affect every attack made on this turn, but rather that it applies to "an attack". I read this to mean that you essentially get to choose before each attack you make as part of either your Multiattack: Volley action or your Attack action (with Extra Attack). As applies to the entire question - nothing about Sharpshooter says it applies to your turn or your action, simply "an attack", any attack (it could even apply to an attack you make as a reaction outside of your turn).