My area of study is actually the time after the Bible (Late Antiquity/Patristics), so I will comment a little on the first two, with the knowledge I have. For further information on these, i'd suggest posting this to /r/academicbiblical, which will have a higher concentration of specialists in New Testament Studies.

When were the gospels written - is it true that we have evidence of all of them being written prior to 80 AD? (my friend claimed this and I am not sure if I believe him)

The popular view in biblical scholarship is Markan priority, in which Mark is placed as the oldest gospel. The general time in which it was written is viewed to be 70 AD.

Matthew and Luke are often argued to be based in part on the Mark-text, with at least one other source in play (most say 'Q' source), so are probably written afterwards, and I would suggest 80 AD is a good estimation, but most likely before the close of the first century, anyway.

John's the black sheep of the group, and was probably written right at the close of the first century.

In short, then, in answer to your first point: No, the gospels were likely not all written (in their entirety at least) before 80 AD.

How credible is the tradition that they were written by Mark, Matthew, Luke and John? Are they all just anonymous? Are any of them first hand accounts?

Not very credible, to be honest. The source for a some of these claims (especially about G-John) seems to be the now lost text of Papias' Five Volumes of the Sayings of the Lord, also called Expositions of the Sayings of the Lord. It was well known to many of the Early Church Fathers, and survives in parts through quotations in Patristic sources. However, sadly, it is lost to us.

It's well-attested to in Eusebius' Ecclesiastical History, but as this work was written between 300 and 320 AD, it's a little late to be wholly credible, and is influenced by two centuries of traditions seeking to cement the apostolic authority of the Gospels.

Because of the current scholarly concensus on dates, it's very unlikely that they were written by the Apostles, though perhaps there is an argument to be made for John, who may or may not have lived to a very advanced age in Ephesus. This, however, remains pure speculation.

So, in answer to your second question, not really that credible!

Is there any clear evidence that they have been altered and revised for theological purposes since they were first written?

Additions to the New Testament do happen, and they can be for theological reasons. My personal favourite example is not from the gospels, but from 1 John 5 (the fact it's only found in Latin is of particular note):

et tres sunt, qui testimonium dicunt in caelo, pater, verbum (or filius) et spiritus, et hi tres unum sunt.

And there are three, who speak testimony in heaven, father, word (or son) and spirit, and these three are one.

This addition is quite evidently there to cement some kind of Trinitarian (or at least proto-trinitarian) doctrine as scripturally sound. This is found in the textus receptus, but not in the codices Vaticanus and Sinaiticus.

So, we have a clear addition for doctrinal purposes here.

A possible example is an addition to Matthew 18:11 that is omitted in most modern translations:

For the Son of man is come to save that which was lost.

A clear reference to recapitulation, the doctrine of original sin, and other forms of theological ideas of Christ as redeemer, I'd argue that this addition could have been intended in no way other than to make scripture more obviously advocate the redeeming aspect of Jesus' life and death (as a Christian, I would suggest it's pretty obvious anyway, but I digress).

This addition alone demonstrates it's been done to the Gospels.

So, in response to your third question, abso-bloody-lutely! There are a bunch of these, and the best way to see it would be to compare the KJV with translations based on Nestle-Aland or other modern critical editions of the New Testament.

There is tons of unbiased scholarship on this topic, and you could get very deep in sources if you wanted. I would suggest Bart Ehrman from UNC as your most accessible popular writer. His book Misquoting Jesus would be a great place to start.

In short order, most scholars will answer your questions:

No, Mark was written first, and only just before that date, the rest were (in order): Matthew, Luke, John. John's gospel was completed well into the second century AD.

No, there is absolutely no evidence, and is completely unlikely they were written by their eponymous apostles and disciples. None are first hand accounts. Mark was written at least 30 years after Jesus died.

There is tons of evidence they have been significantly altered, combined, and revised. Again, use Ehrman's book.

Hope this helps.

Edit: 30 years after Jesus' death