Regarding the Vikings in North America, the main problems for the tentative thrust into 'Vinland' and the Newfoundland settlement shown in the sagas seem to have been the lack of 'committed' Scandinavian personnel, the insecure nature of the first settlement due to the unexpectedly large amount and military skill of local (Athabascan?) resistance, and the lack of a major commercial product to acquire and sell off profitably back in Greenland/ Iceland/ Norway. There was just not enough profit or security, or long-term commitment by capable leaders, to keep up a presence in L'Anse aux Meadows or to move on South via Nova Scotia to Maine and Massachusetts. At this point, the climate on the W coast of Greenland appears to have been equable enough to enable the settlers there to keep large herds of stock and the Inuit presence small enough to avert any major danger of raids and reconquest, so it was safer to keep the Westernmost Viking outposts in the Americas in Greenland. (NB: did any adventurous but now forgotten voyagers go seeking trade up the North-West Passage islands around the N of Canada before the climate worsened and the ice was covering it all year round in the 'Little Ice Age', and stories of a navigable Passage were passed down through the generations and duly inspired the Elizabethan searchers and Henry Hudson?)
A larger and viable Viking settlement in the Americas might be possible on the basis of larger numbers of landless personnel involved and no room for them in Greenland - where crops could probably not be grown anyway even around 1000. I propose that possibility in my 2011 Pen and Sword book 'If Rome Had Survived' on the timeline of a surviving Roman Empire being infuriated by Viking attacks on Britain, Ireland and Gaul and attacking and overunning Denmark and raiding Norway in retaliation, using a technologically advanced navy with 'Greek Fire', the OTl naptha-like secret weapon used by the Byzantines against the Arabs. That way, those Danes and Norse who don't want to submit to Rome move en masse to Iceland and thence the Americas and settle in Massachusetts and Connecticut - where the forests would look familiar to the Scandinavians and a mass of war-ready Vikings with swords and axes could overwhelm the locals. Another group of Vikings explore up the St Lawrence, do portage round the Niagara Falls like they did in OTL on the Dnieper, and start fur-trading W of the Great Lakes.A few centuries later the Romans arrive in the 'Old South' of the US via the Caribbean and start fighting them over land, and as the Romans push North we have war in the New England area...
This motivation for a larger-scale and self-sustaining settlement of farming lands in the NE United States or up the St Lawrence would need a major demographic 'push' by a European power to shift personnel out of Scandinavia and induce them to head NW, not to divided and land-rich Ireland to settle. In OTL it seems that the unification of Norway and expulsion of his warlord enemies by King Harald 'Finehair' in the later C9th drove some of the exiles to settle in the Shetland, Orkneys and Hebrides and possibly the Isle of Man. So if we have something similar on a larger scale in slightly later Scandinavia, when the Americas have been discovered and rumours of its riches (exaggerated by spin?) as 'Vinland' are being circulated by visitors, we could get a reasonable-sized expedition there - there is no room for the exiles in smallish and partly infertile Iceland. At this point, Norway is only precariously united and frequently breaks up or suffers civil wars. Perhaps if there is a major war or purge there, the 'loser' faction could have to leave en masse to avoid massacre or starvation. One possibility is if the regional strongman Cnut 'the Great' ( ruled England 1016-35, Denmark 1014/18-35),is able to take Norway back by force after his unwelcome conquest of 1028/30 and imposition of his son Swein as its puppet-king leads to a major revolt in 1035. in OTL the exiled prince Magnus is welcomed back by anti-Cnut plotters and Swein's regime is expelled, then Swein dies (or at any rate disappears from the record) and Cnut, aged at most around 45 and possibly only 40, dies later in 1035 and cannot invade. A civil war in England between Cnut's other sons then stops any reunification of his empire and his surviving son by Aelfgifu of Northampton, Harold 'Harefoot' (Swein's full brother) secures England in 1036 while Cnut's son by Emma of Normandy, Harthacnut , secures Denmark and fights Magnus of Norway. But if Cnut is in full health and as ruthless and bloodthirsty as he was in his wars in England in 1014-16, he could use his Anglo-Danish fleet to reconquer Norway by force and kill or expel all his foes there, driving many elite warlords and their warriors out into exile. There is no room in the Orkneys or Iceland, and if we have a stronger Gaelic victory over the Irish/ Orkney Vikings at the battle of Clontarf in 1014 (and aged national unifier King Brian Boru succeeded by his capable son Murchad as High King) the Vikings have no secure lands in Ireland either. So a Norse expedition - under deposed king Magnus or his senior jarls? - could head off as a suitably huge gamble to the 'empty' lands in North America to settle there. Then if that settlement is large enough to be self-sustaining and can export timber, furs etc back via Greenland to Iceland and Europe it could survive long-term as a chain of settlements down the coast from Newfoundland to the Cape Cod region, and as the ice thickens the Greenlanders move there.
For that matter, given adequate information about the routes and regular trade there are other bodies of exiles from NW European military catastrophes that could head off to this region, In OTL a large group of Anglo-Saxon warriors from conquered England after 1066 headed off to Constantinople to join the Emperor's Varangian Guard and in 1081 were found fighting as a regiment for Emperor Alexius Comnenus against invading Normans (from Italy) at the Battle of Durazzo in modern Albania. (Now there's a theme for a series of adventure novels...) In reality, after King William put local revolts down in N England in 1068-9 a lot of the Anglo-Saxon resistance and their pretender to the throne, Edgar Atheling, went off to Scotland where E's sister (St) Margaret married king Malcolm/ Mael Coluim III. What if they had headed off via Orkney to the Americas instead of to Byzantium?