The answer to the question in your title is that it depends on what you (and Herodotus) mean by 'dark-skinned'. There is certainly no evidence of any large black African population in Colchis (contrary to the claims of many afro-centrists).
The quotes from the Quora answer will be dealt with individually below.
Firstly, your question:
Pindar, Apollonius, Pliny, Jerome etc. Did these men really write these things as quoted above?
Well, let's deal with each pf the quotes in turn.
In 522-443, a Greek poet named Pindar described the Colchians as being "dark skinned with woolly hair".
Pindar was one of the first Greek authors to refer to Colchis by name in his Fourth Pythian Ode. The description of the Colchians as being "dark skinned with woolly hair" does not appear anywhere in the poem.
It seems that Chadwick Tyroné, the author of that answer on Quora, is actually ascribing a quote from Herodotus to Pindar.
Apollonius of Rhodes states that the Egyptians of Colchis preserved as heirlooms a number of wooden tablets, which show, with considerable accuracy, seas and highways.
That line (with that exact wording) appears on the Wikipedia page for Colchis, but without citation. If you enter the phrase into Google you will find hundreds of sites using exactly the same wording (that's the power and reach of Wikipedia).
However, if I remember correctly, the only surviving work by Apollonius of Rhodes that mentions Colchis is his epic poem Argonautica, which tells the story of Jason and the Argonauts and their quest for the Golden Fleece. The text is available from a number of online sources, including this copy on archive.org. Notwithstanding the oft-repeated claim on Wikipedia, the people of Colchis aren't described as 'Egyptian' anywhere in the text of Argonautica.
"According to Pliny the Elder : The Colchians were governed by their own kings in the earliest ages, that Sesostris king of Egypt was overcome in Scythia , and put to fight, by the king of Colchis, which if true, that the Colchians not only had kings in those times, but were a very powerful people."
It is certainly true that Pliny the Elder made this claim in Book XXXIII of his Natural History. The king of Colchis who is supposed to have defeated Sesostris (although not in Scythia, as claimed on Quora) is named as Saulaces. However, as noted in the Wikipedia article:
"Pliny's account of Saulaces and his victory over the Egyptians is uncorroborated by other written sources".
It is worth noting that there is also no archaeological evidence to support the claim.
350 to 400 AD, Church father St. Jerome and Sophronius referred to Colchis as the "second Ethiopia" because of its black population. [From: Patrick T. English, Cushites, Colchians, and Khazars, Journal of Near Eastern Studies, vol 18, Jaunuary - October 1959, p. 53.]
Now, Patrick English's paper is available on JSTOR. He does indeed make that statement, and the footnotes claim that the source is ultimately Samuel Bochart's Geographia Sacra (Book iv, xxxi). But that isn't actually what Bochart says:
"Ptolemaeo Sebastopolis eadam quae Dioscurias, Colchidis emporium olim adeo clarum, ut trecentae in illud nationes que dissimilibus linguis uterentur, mercaturae gratia confluxerint. Ita ex Timosthene Plinius, qui addit a Romanis CXXX interpretibus negotia ibi gesta. Itaque hoc manet Colchis Aethiopum nomen inditum ab Hieronymo, & Sophronio."
And, a black Colchian writer, historian, and ethnographer, Dmitri Gulia (1874-1960) asserted that his heritage originated from Sesostris. He published a book called, History of Abkhazia, which shows that the black Colchian people of Southern Russia were really an Abyssinaian people of Egypt. He shows putting together a vast array of Abkhazian words that matched that of ancient Egypts is more proof for it. (Poe, 58)
This is an interesting one (and another of those claims where the exact wording can be found on dozens of other sites).
Black Athena by Martin Bernal was required reading for one of the courses when I studied Egyptology (followed by weeks of detailed analysis and evisceration of the text!). The first part of this claim, about Guila's heritage, appeared in Black Athena. Despite the fact that Bernal quoted Dmitri Gulia in his text, Gulia's book did not appear in Bernal's bibliography (and, as our tutor was at great pains to point out, this is often a red flag that something may be amiss!).
I haven't read Dmitri Gulia's History of Abkhazia (it may never have been published in English, or even outside the Soviet Union, and so far I haven't been able to locate a copy online), so I can't comment on what he actually did or didn't claim in the book. He may indeed have asserted that his heritage originated from Sesostris, but that simply shows that he had read, and believed, what Herodotus wrote in his Histories.
However, even Martin Bernal never claimed that Gulia had proved that the black Colchian people of Southern Russia were really an Abyssinian people of Egypt.
Now, for your second question,
Is Herodotus disproved or validated on his claims about a dark skinned and woolly haired people living in Colchis?
The first point to note when dealing with any ancient author is that the reliability of their claims generally diminishes as the distance between the author and the events they are describing increases, in terms of both time and geography. Now, in this case Herodotus actually says:
"... when he came to the Phasis river, that King, Sesostris, may have detached some part of his army and left it there to live in the country (for I cannot speak with exact knowledge), or it may be that some of his soldiers grew weary of his wanderings, and stayed by the Phasis."
"For it is plain to see that the Colchians are Egyptians; and what I say, I myself noted before I heard it from others. When it occurred to me, I inquired of both peoples; and the Colchians remembered the Egyptians better than the Egyptians remembered the Colchians; the Egyptians said that they considered the Colchians part of Sesostris' army. I myself guessed it, partly because they are dark-skinned and woolly-haired; though that indeed counts for nothing, since other peoples are, too; but my better proof was that the Colchians and Egyptians and Ethiopians are the only nations that have from the first practised circumcision."
The first point to note is that Herodotus would fail the History:SE requirement for citations to support his assertions! These days, the claim that "a couple of blokes in Colchis and Egypt told me ..." would not be a sufficient citation! (Indeed, Herodotus' willingness to believe and repeat the stories he was told is one of the main reasons he was also given the epithet "The Father of Lies").
Secondly, if the people of Colchis were indeed descended from a part of an Egyptian army that remained following the conquest of Sesostris (a 'conquest' for which we have absolutely no record in Egypt), then they were a very remarkable group in that it would appear that they did not preserve any aspects of their highly distinctive Egyptian material culture, burial practices etc.
Thirdly, by Herodotus' day Colchis was part of the Persian empire. As the Wikipedia page notes, Colchis had been invaded and defeated by the Assyrian empire, and was subsequently incorporated into the Achaemenid Persian Empire toward the mid-sixth century BC. There are thus a number of possibilities for the origins of the 'dark-skinned' people that Herodotus claimed that he saw in Colchis.
Finally, if you look at the Greek, you will see that the word translated as 'dark-skinned' is μελάγχροες or melanchroes (which can mean anything from a healthy, bronzed tan to black), and the word translated as 'wooly-haired' is οὐλότριχες or ulotrichous (more often translated simply as 'curly-haired'). So exactly what he meant by that description is unclear.
Finally, to deal with the broader question in your title:
Is there any evidence in history to suggest that there was a Melanchro (dark-skinned) population in Colchis as claimed by Herodotus?
As discussed above, this really depends what you (and Herodotus) mean by 'dark-skinned'. What we can say is that there is no evidence of any large black African population in Colchis, or, indeed, anywhere in the Caucasus.
Although work in this area is ongoing, to date, studies of Mitochondrial DNA and Y-Chromosome Variation in the Caucasus have shown no evidence for any significant black presence in the region.
Obviously, one might expect that any substantial black population in Colchis would be reflected in the DNA of the modern population in the region. Since the DNA shows no such evidence it seems that whatever Herodotus meant when he described the people of Colchis as μελάγχροες and οὐλότριχες, it could not have been black Africans!
Incidentally this DNA evidence also demonstrates that modern afro-centrist claims that this line in Herodotus proves that there was a black African community living in what is now modern Georgia are completely unfounded. Furthermore, the claim that, by extension, this line in Herodotus proves that the ancient Egyptians were black must also be wrong. If anything, it suggests that the Egyptians of Herodotus' day looked like the people of Georgia!