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.
Yes, you get assassinate and sneak attack.
No, the critical would not apply to the fire damage.
Let us assume the DM allows you to craft this contraption, possibly giving it a -2 to hit or something of the sorts due to its unwieldy nature.
PHB, page 96, Sneak Attack:
Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.
Sneak attack is applied on any attack roll with advantage as long as it is a ranged or finesse weapon. A bow is a ranged weapon.
PHB, page 97, Assassinate:
You have advantage on attack rolls against any creature that hasn't taken a turn in the combat yet. In addition,any hit you score against a creature that is surprised is a critical hit.
We have our advantage and critical against a surprised creature that hasn't taken their turn yet.
PHB, page 196, Critical Hits:
When you score a critical hit, you get to roll extra dice
for the attack's damage against the target. Roll all of the
attack's damage dice twice and add them together... If the attack involves other damage dice, such as from the rogue's Sneak Attack feature, you roll those dice twice as well.
The key phrases here is when you score a critical hit. You would roll double the damage dice for the hit on the turn you hit the creature (including double the sneak attack damage), but at start of each of that creature's turns you would roll the 1d4 fire damage separately without doubling it.
Best Answer
RAW, these improvised weapons probably do not deal the normal 1d4+DEX damage.
Each of these objects specify that the user should treat them as an improvised weapon while making their special attack, which would imply 1d4+DEX damage on a hit. However, they also specify what should happen if the attack roll is a hit, such as the acid vial dealing 2d6 acid damage as you mentioned. This specific effect replaces the general effect of landing the hit.
While it would certainly make sense that being beaned by a glass bottle would deal damage, all of these hit descriptions are missing the important word extra when they are describing their on hit effects. All of the effects that I could find which have an attack deal damage on top of its usual damage, such as the Rogue's Sneak Attack feature, the 5th level enhancement of the greenflame blade cantrip, and magic weapons such as the Frost Brand list the damage as extra damage. If the vials were intended to also deal their improvised damage, they would have their effects listed as extra.