The surviving writing in Ireland from the 4th century consists of mere epitaphs or territorial markers written in the Ogham script. There's no direct evidence of other usages of the script or consensus of how widely used it was at this time.

The Irish learned Class were committed to Oral Tradition. A great memory was one of the most impressive aspects of being a Bard or Scholar, more so than writing. I don't think enough is known about the Druid class or how one became a druid to give a factual answer for that profession. I'll focus on the bards.

Basically, Irish society formed a strict caste, based on the status of your grandparents. The only way for a family to move up in status was to acquire more wealth, and to maintain that wealth for three generations. Then your grandchildren would enjoy more societal privilege. So it may seem unlikely that a farming family (there were several ranks of free farmers and unfree serfs) would give rise to a bard. But not impossible.

The Bardic Schools were run by the highest ranking bard called an Ollamh. There were places for paying and non-paying students which indicated some common people studied. It's possible that non-paying students graduated at a lower rank - I haven't found a clear source for that. There were seven grades of Bard who entertained the appropriate social class.

A curious tradition known as literary fosterage existed. Occasionally the Ollamh adopted some students into their own family - Irish law took fosterage very seriously - legally the fostered children gained the status of their foster parents.

Unprofessional or informally trained bards are also mentioned but they would only recite poetry and would not compose.