Your question doesn't break it down this way, but there are really three separate issues at stake here.
What does the Gospel of Barnabas claim about Christ?
The most significant claim relevant to Christianity is that Christ wasn't crucified. Instead, according to the Gospel of Barnabas, Judas took his place. Obviously if this were to be verified as a true representation of historical events it would have major implications for the Christian faith.
If you really want to know what it says, the contents of the book itself are public record (html English translation, scanned pages of early translation with a couple original Italian samples); you don't need to pay $2 million a page for photocopies. That's tabloid reporting.
Are the claims in the Gospel of Barnabas and its doctrinal positions legitimate? Do they present a challenge to the historicity of the claims in the four canonical gospel texts?
In a word, no.
The first known mention of its existence is from 1634. The two earliest known manuscripts are from the 16th century and an Italian document and a partial translation to Spanish. Mentions of an Arabic text are generally agreed to be later translations of this text; no earlier copies have ever been found or even mentioned. (Not to be confused with mentions of other quite different texts involving Barnabas, to be explained under the next heading.)
It's fairly clear to anybody who studies them that they do not represent content from the Biblical Barnabas. At most it is alleged by a small subset of Islamic scholars that it contains traces of suppressed apostolic material. Wikipedia summarizes the state of scholarly opinion like this (see article for sources):
This Gospel is considered by the majority of academics, including Christians and some Muslims (such as Abbas el-Akkad) to be late and pseudepigraphical; however, some academics suggest that it may contain some remnants of an earlier apocryphal work (perhaps Gnostic, Ebionite or Diatessaronic), redacted to bring it more in line with Islamic doctrine. Some Muslims consider the surviving versions as transmitting a suppressed apostolic original.
In evaluating the merits of any text claiming to be historic, one must put it in context with other known sources. If a large number of eyewitness or early accounts are attested by multiple sources that are otherwise considered trustworthy conflict with a single late source of unknown veracity, doubt is automatically going to go to the latter. In the case of the Gospel of Barnabas, the manuscript gives us nothing to go on. In fact sources from the 100 years following the first mention of such a text treat it with no particular respect except as a rehash of Islamic dogma from the era.
In spite of the lack of historical weight, you will hear a lot of hoopla about it. Living in Turkey myself it's a popular source for Muslims to cite in support of their version of history. But here's the thing—the Muslims citing it are the uneducated variety from the streets and a few whack-job apologists. This does not mean Islam as a whole supports the work of uses it as a reference. Ask a respected Islamic scholar with an iota of credit in history and they will usually reject the book as being a fraud. I have, for example, conversed with the Dean of History at the Islamic Divinity School in Izmir, Turkey. While he supports the Islamic version of events including Judas being the one crucified in Christ's place, he rejects the Gospel of Barnabas as valid evidence for such.
Does the 1500 year old manuscript find from Turkey include the Gospel of Barnabas?
No.
This find is actually old news. If memory serves me it's from 1985 and is supposed to be remarkable for its state of preserve, but it does not include the Gospel of Barnabas or any other texts not considered Canonical by modern Christians so it has no particular implications on the content of "The Bible" or our understanding of history.
In fact if it were to have contained any non-canonical sources it would be far more likely to have included what is known as the Epistle of Barnabas (English text). That work is something that could have actually existed in the alleged time period, language and location of the find. This would have been interesting esp if it had a complete copy as the extant manuscripts are all missing some of the first chapters of that work. This work is sometimes attributed to the Biblical Barnabas, but as the contents of the text exhibit Gnostic doctrine it's highly probable that it was written by another author, possibly Barnabas of Alexandria. In any event, the Epistle of Barnabas does not disagree with the canonical Scripture accounts of the historical Jesus' death. Even if it had been included in the manuscript find in Turkey the only thing it would be evidence of is of 5th century Gnostic sects using both canonical and other texts together. No particularly doubt would be cast on the historicity of the other gospel, only on how mixed up the theology of some groups had gotten.
The only really interesting aspect of the manuscript found in Turkey is that it was an early text in Syriac, a derivative of the Aramaic language that Jesus spoke. This makes it an interesting artifact for study—especially for those involved in the Aramaic primacy debate—but again it has no particular implications for the validity of the Bible as we know it.
The manuscript was not very well looked after in the years following it's discovery and changed hands a few times, eventually falling to black-market antiquities dealers. It was eventually recovered in 2000 and made waves in the news then. In the last decade or so most of the news articles about it are rehashes of the tabloid style sensationalist statements printed over a decade before and most don't bother dealing with the actual issues or known state of scholarship.
The manuscript you asked about would have been interesting if it has a Syriac version of the Gospel of Barnabas from 1100 years before it is thought to have been penned, but it doesn't. The whole affair as related in the articles you link is about as fact-based as an episode of Indiana Jones.
