I think the topic has come up in the past here.
I came across this just now: (while, as usual, looking for something else)

http://www.darkfiber.com/blackirish/

But is fidhchell a genuine Irish game, or is it an imported version of the Viking hnefa-tafl?

I think it must have been Irish and not a Viking import because it is mentioned in manuscripts that predate Viking settlement in Ireland in the 9th century. Sure, Vikings were known in Ireland before that date but as raiders rather than settlers. It's unlikely they would have taken the time to introduce a board game during a raid.

Why are there so many Viking finds (also wooden and woollen finds), while in the whole web I haven't been able to find an Irish one?

There have been hundreds of Irish finds from the Stone Age, Bronze Age, Iron Age and right up to late medieval times. If you're talking specifically about the Viking period, among the most famous finds are the Ardagh chalice, the Tara Brooch and various reliquary shrines. Although the Book of Kells was written in Scotland, it was done by Irish monks and is usually regarded as Irish. From a slightly later period (12th century) is the Cross of Cong. You should be able to find web-sites that deal with them. The National Museum in Dublin has many more less well known pieces from the period. Unfortunately it doesn't seem to have a web-site yet.

What of the Bronze shield, chariot fittings and the gold spear found in Lough Gur? Wish I could find a gold spear.

Did the ancient Irish people have contacts with the Mediterranean civilizations?

Several bronze shields have been found in Ireland, Daryl, but I didn't mention them because Guest seems to have a special interest in the Viking period. The Lough Gur finds were made when the level of the lake dropped and objects that had been cast into the lake as votive offerings were uncovered. Most date from the late Bronze Age which is about 1000 years before the Vikings first raided Ireland.

Guest, it depends on what you mean by 'ancient Irish.' How far back do you want to go? Many Neolithic and Bronze Age artifacts found in Ireland are similar in style to those of continental Europe. Stone axes, arrow-heads, spears and other tools are similar. Irish Bronze Age swords, spears and brooches are similar too. Some Halstatt-style Iron Age pieces (approx. 5th century BCE) have been found in Ireland and it's known that the early European Celts traded with Etruscan and other Mediteranean cultures, so it's at least possible that the Irish of the time had contact with them too.

There's a good deal of evidence that wine was imported to Ireland from the Med. The route was quite likely from Marseille, through Gaul, and then either through Britain or directly to Ireland. It's probable that traders travelled between Med and Ireland and culture was exchanged as well as goods. It's the most likely way that Christianity came to Ireland long before Patrick arrived.

But, I mean, have, for example, the Greeks ever been in Ireland?

In ancient times? I don't know of any references in the Annals nor of any archaeological evidence to indicate that Greeks ever settled in Ireland. That it was fairly well known to Mediterranean people is shown by Ptolemy's map of Ireland (about 150 CE) which gives the names and locations of some of the tribes on the island at the time.

There is some evidence, although it is disputed, that at least some Romans settled in Ireland. A burial containing a man, a woman and Roman artefacts was found in Co. Kilkenny (I think). They could have been either a Roman couple or an Irish couple who had lived somewhere in the Roman Empire and had accumulated the artefacts there.

Being a hopeless romantic for the old tales, I always have kind of thought that since the chariot fittings were found off shore quite a bit, that it might have been the remnants of the chariot driven by the one legends say attempted to steal the Brat Uáine from the Axis Mundi. Far reach, I realize, but anything is possible.

No harm in being a romantic about the old tales, Daryl.

The mythology surrounding Aine (Anu) and Danu is very complex. Some think they are the same deity. Others think they are different. My own leaning is towards Anu being a pre-Celtic Irish goddess and Danu being later Celtic introduction.

As regards the chariot fittings found offshore at Lough Gur, the most likely explanation is that they were votive offerings.

I have wondered about that(Danu vs Anu), but I class the subject in the group of things I will probably not get a chance to explore enough to draw a conclusion for myself.

To add another level of complexity to the controversy, I have read several books that have claimed that Brigid and Danu were the same person.

The "names" of many Celtic goddesses aren’t names but titles. "Brigit" probably means "High One" or "Exalted One" and is therefore a description rather than a name. Similarly, Boann (Boand) after whom the River Boyne is named, means "she of the white cows" or something similar. Brigit, Anu and Danu were possibly different titles for the same goddess of fertility and fecundity. Brigit was identified during Roman times with Minerva because both were associated with crafts and with healing. I’ve seen suggestions that sheela-na-gigs are representations of Brigit.