My list of papyri discoveries is a little dated. Has any new papyrus been found from the 1st. cent. that one of the immediate disciples of Jesus wrote? It would be in Aramaic, I expect. There was a mention of a Gospel by Matthew, made by one of the Church Fathers that was in Aramaic. but it has not been found.
Nope. The earliest manuscript fragment we have is p52. It dates to about 20 years after John wrote it.
And, while it is likely that the apostles spoke Aramaic, there is nothing to conclusively prove they wrote in it.
In any event, the apostles wouldn't have written it in their own hands. Most writing was done by an amanuensis - a guy who made the paper and ink, and wrote down what he said.
The one exception to the amanuensis is most likely when Paul writes "See what large letters I write in my own hand".