Mage hand can pour out a vial of acid.
Pouring a vial of acid in this way will (generally) not damage an enemy.
It's exactly as the rules you quoted say. You can pour out the contents of a vial. Per the description of Acid, simply pouring isn't enough to do someone--who likely doesn't want acid poured on them--damage.
If you start pouring acid on one who doesn't want to be acidified, they can move, interpose an object, or otherwise evade the damage. In order to damage someone with acid you've got to splash it onto them, an activity that's defined as a ranged attack. And Mage Hand, per its description, can't effect damage on someone trying to not be damaged: it can't attack.
Could one pour the vial over an unsuspecting enemy, or one incapacitated or restrained, thereby causing them damage? I contend it follows the same rules: if you would need to make an attack roll, Mage Hand can't do it. Whether those situations require an attack roll--and therefore are attacks which Mage Hand cannot effect--is a ruling to be made by the GM.
This spell is the only official mention of "Unholy Water"
A quick search on D&D beyond, the official D&D 5e web toolset, reveals that the Commune spell is the only official mention of the term "unholy water".
That means we have to fall back on natural language
Since the term has no official game meaning (because it is only mentioned once as a spell component and nowhere else), we have to use the natural language definition of the terms.
Unholy water is, obviously, water; it's in the name.
Dictionary.com defines unholy as:
1.
not holy; not sacred or hallowed.
2.
impious; sinful; wicked.
By this definition, unholy water could just be water the isn't holy water. However, this would mean that something like tap water could be used as the material component of the spell. Since, Commune specifically allows you to talk to a deity or divine proxy, I would argue that this non-religious/non-divine definition isn't what is intended.
So, based on the second definition, unholy water is some way the opposite of holy water. Where holy water is water that is blessed and carries a positive religious connotation, unholy water is profane, wicked water with a negative religious connotation.
RAW however, that means unholy water doesn't do anything
As you have noted, there are no rules for creating "unholy water". There are no descriptions of any mechanical effect that it has, or any uses for it besides this one spell. RAW, it is simply used for the Commune spell and nothing else.
It has no other properties RAW, and any other mechanical effect given to unholy water would be a DM call.
Best Answer
Yes, the attack is made at disadvantage; the only difference is what happens to the flask
As stated in your quote, regardless of whether you splash the contents of the flask at a creature within 5 feet or throw it at a creature up to 20 feet away, you make a ranged attack.
The rule on making a ranged attack with an enemy within 5 feet of you says:
(One of the benefits of the Crossbow Expert feat (PHB, p. 165) is to eliminate this disadvantage.)
The only apparent reason the two methods of making this ranged attack are called out separately is what happens to the flask when you make the attack. If you splash the contents of the flask onto a creature 5 feet away, the flask remains intact and in your hand; only its contents (holy water or oil) are splashed onto the creature. On the other hand, if you throw the flask at the creature, it shatters on impact and can't be recovered, causing its contents to splash against the target if it hits.
As Akixkisu's answer notes, oil can also be poured onto the ground directly and lit on fire that way:
And holy water can also be poured on the ground directly to purify desecrated ground (DMG, p. 110):
Neither of these is an attack, and they involve no rolls. In the absence of anything specifying whether they take an action, this can likely be done with a free object interaction, or the Use an Object action if that has already been used.