It is not known (with the exception of Luke) with certainty who wrote the gospels and if they were not written under pseudonym (a frequent method used at the time through which the one who wrote wanted to give to his writing the vision of an emblematic personality).
how can an anonymous Gospel be written under a pseudonym? It was not in fact a frequent method in 1st century AD and in later centuries was rather the practice of heretics who wanted to bolster up their own teachings with a name.
Why should you think it more likely that Luke wrote Luke than that Mark wrote Mark? Both were unlikely names to add to a Gospel and supported by early tradition. Thus both are almost certainly correct.
There are a number of evidences within John's Gospel that it was written by John. For example he is never referred to by name in the Gospel (an almost inconceivable thing for any other writer to do), and he refers to John the Baptist simply as John, not feeling it necessary to identify him. The writer also had the favoured place (as Jesus' cousin?) at the Last Supper.
These writings have not been written immediately after Christ' ascension. The earliest ones (1 Thessalonians and Mark) were probably written 35-40 years after the events.
It is generally recognised by most scholars that 1 Thessalonians was written around 41 AD.
Before this, the narrations circulated orally,
The stories of Jesus' life, taught in the churches by the Apostles, would take on a fixed form and some of these were probably put into writing very early on to be passed on to other churches. In the early days the churches preferred to hear the accounts of eye-witnesses rather than trust writings which could have come from any source, unless the source was well known. Those accounts would then be passed on in a fixed form which was constantly checked as Apostles visited the churches.
in various versions until Mark (?) decided to make a synthesis of them;
But Papias (who was in a better position to know than us) claimed that Mark went around with Peter and thus wrote down the eyewitness evidence of Peter. 'Oral tradition' is a dangerous idea. Whose oral tradition? The oral tradition of Peter, no doubt coming under the scrutiny of other Apostles, was no doubt of first importance. And that was Mark's source.
he might have used the famous Q source which no one found, but this is just a hypothesis
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And is now very much questioned.
Luke and Matthew wrote using the text of Mark as source
This is no longer so confidently asserted. There are good grounds for thinking otherwise. Both Matthew and Luke have much independent material and comparison of Matthean speeches with Luke's throws grave doubts on whether they came from the same written source. As a trained recorder it must be seen as extremely likely that Matthew wrote down Jesus' sermons, thus their Aramaic flavour. Luke would have derived his from eyewitnesses during his long periods in Palestine..
John is a late writing (like you said) which was written in another context than the first three synoptic gospels.
There are actually no real grounds for suggesting this. The assumption is usually made because it is seen as 'more spiritual'. But are we really to suggest that anyone was 'more spiritual' than John? Later writers give the impression of being less spiritual. It was clearly written by someone who was in on the disputes with the Pharisees by a man of spiritual bent. There is no justification for making it especially late.
What should be noted is that the Gospels appear to have had their titles from almost the beginning. We must not assume that the early church lived in the dark. THEY KNEW WHO WROTE THE GOSPELS, The titles were probably added by them attached to the papyri and manuscripts so as to show what was written in each document. And the universality of the titles indicates an early date. Thus we have good reason to think they were written by those named. The early church were not gullible.