Balancing Your Feat
I don't think it's terribly well balanced; in most cases, it's actually weaker than a feat:
If you take the first option twice, it's the same as a basic ASI.
If you take either the second or third option, it is strictly weaker
than Skilled (PHB p170), which allows choice of three skill or tool
proficiencies.
Take the first and last option, and it's weaker than Linguist (PHB
p167), which provides +1 Intelligence, three languages, and the ability to
create coded messages.
Feats are supposed to be powerful, and your design is watered down in comparison. Feats also tend to be packaged abilities with a theme, selecting one makes a character different from others with the same class. Were I playing in your game, I wouldn't take anything but the ASI, which I could do anyway.
There are also stacking concerns - normally, the same feat cannot be taken more than once. If this is the only feat available in your game, then it's clearly stackable. It allows a player (over time) to stack a large number of skill proficiencies, potentially having proficiency in everything, which will trivialize skill checks and reduce each character's uniqueness.
The Power of (Variant) Humanity
Variant human is pretty powerful, but so is a normal human. I think you're overlooking the raw strength of solid attributes. Having a bonus to six stats shores up potential weaknesses and/or saves points the player can spend on the character's desired strengths.
New Player Advice
If you're trying to ease new players into the system, you could disallow "Variant Human" completely. That would push off selection of feats until L4 at the earliest (if you allow them at all, they're entirely optional), and allow some time for people to get used to the basics.
The issues you might have
This is written assuming you go for method 1 or 3, or you go for method 2 and the players roll a good set of stats. Personally, I'd avoid method 2, since it has a lot of ways to go wrong that nobody would be happy with; if you want to give them a powerful array, just let them have one that you decide on, and then you know what level they're on.
Increased power level
In general, letting the PCs have higher stats like this - and all of your proposed methods let them potentially start with an 18, assuming an appropriate race - allows the PCs to have about a +1 to hit and a +1 to damage. This makes them a bit over 5% stronger offensively, and probably another 5-10% stronger defensively because of increased saves and hit points. This probably equates to about .5 of a CR in terms of how challenging encounters will be.
Skill check DCs are by comparison easy to adjust - just expect your players to always get 1 higher than average characters of equivalent level.
Flatter top end
If everyone is special, nobody is. That is to say, if everyone gets to start with an 18 in the stat that they care about, it's not nearly as special when somebody reaches 20. Bear in mind that the items and abilities that set your ability scored are designed with "standard" player characters in mind, so a wild-shaping druid may feel underwhelming since their wild shapes are less effective than other players, and items like the amulet of health are less wondrous.
Feats everywhere
With the need for ASICs to be spent on stats massively reduced, your players will definitely want to take more feats. Some feats (such as Sharpshooter) are massively beneficial in combat, sufficiently so that if they play things smart they might be hitting a full CR above their level.
So what do I do?
There are a few paths; feel free to mix and match from these options as well.
Adjust the world upwards
The most obvious option is just to deal with it by making things a little harder. You'll probably have to adjust monsters upward occasionally - tweak a few monsters by giving them a unique description and bumping their attacks or defences up by a point, and maybe an extra HD or so.
I'd advise being clear with your players that they're building powerful characters and that you plan to challenge them appropriately from the start.
Let it roll
Specifically, let the players be slightly overpowered. D&D is already positioned for the players to be the heroes overcoming evil; they'll have a slightly easier time of it than most, but they may well enjoy that. You may find this frustrating as a GM if your encounters have difficulty challenging them, but a difference of +/- 1 shouldn't be that bad.
Reset expectations
Tell your players that you want to run a campaign at the standard power level. Make it clear that they're not expected to have or need "optimal" ability scores, and that the standard array/standard point buy will not impede their ability to be adventurers.
Best Answer
The current edit on the question changes the answer significantly.
As mentioned by András, the Sharpshooter is already one of the strongest feats in the game. Adding versatility to it makes a feat that is already "must take" for ranged characters incredibly broken, imho.
You are making it too strong, because it is already strong.
I'll state it again to make it clear: the problem is not exactly your addition, but the fact that the feat is already strong as it is and any addition to it makes it too strong, from my point of view.
You need to add a trade-off
Instead of just making it stronger by adding another option, make it a trade-off. If you want to add another option, then you lose something on the other options. Also, you should make it in such a way that choosing between hitting only one or two targets is actually a choice.
Disclaimer: I have not tried these homebrew-changes to the sharpshooter feat, so the following is theorycrafting. I'm putting these into answer as ideas to the person making the question and to give examples of what I mean by adding a trade-off. The question itself was already answered in the previous section - no, it's not reasonable to add something to the sharpshooter feat and yes it needs more restrictions.
The changes I would make are the both that follow: (Both, not choose one)
The second arrow doesn't add your damage
Similar to Dual Wielding for melee fighters, a possible and easy nerf is to make the second arrow do only the flat damage, instead of the damage plus dex bonus.
The third option of Sharpshooter gets nerfed a little
To +7 or +8 damage. Honestly, it would need playtest to get to an accurate value that makes the trade-off between hitting two targets instead of only one an actual decision instad of "hitting only one is always better" or "splitting is always better when possible".