They’ve actually found ancient encampments in North America which are believed to be Viking. They were fearsome marauders that decimated, murdered and pillaged the British Isles and were the greatest seamen at that time. The Irish druids did their share of pillaging as well but were not great seamen.
L’Anse aux Meadows in Newfoundland is widely accepted by archaeologists as Norse.
http://en.wikipedia.org/wiki/L%27Anse_aux_Meadows
So there is not really any grounds for doubting that the Norse made it here around the Year of Our Lord 1000.
The Irish question is more complicated. To date no evidence of it has been found by modern researchers. However, the Norse sagas contain several references to the Irish or some other Europeans preceding them.
http://en.wikipedia.org/wiki/Hvitramannaland
Who knows. I wouldn’t take the Voyage of St. Brendan as history per se, but wiser scholars than I have noticed it does betray a familiarity with the seas of the northern Atlantic.
About the supposed similarity between Basque and Shoshoni, I wouldn’t give that theory any credence unless it were backed up by not just a few shared roots but by a systematic grammatical comparison. Shoshoni is an Uto-Aztecan language with widespread roots in North America, including Aztec—its grammar is very well known.