1. The Norsemen first appeared in Ireland in 795 and made frequent raids, eventually taking control of two ports and a series of large-scale invasions in the north.
2. The decline of Norse power began when they lost Limerick in 968 and was finally effected when the Scandinavian allies of the king of Dublin were defeated by High King Brian Boru at the Battle of Clontarf in 1014.
3. The Anglo-Norman invasion before Henry II's arrival extended their sphere in Ireland, with O'Connor accepting Henry as his overlord and restyling himself as only the king of Connaught.
The article is generally reliable, providing an accurate overview of the history of Norse invasions and their aftermath in Ireland. It is well-researched, citing historical events such as the Battle of Clontarf and providing detailed information about the political situation after the invasions. The article also provides a balanced view on both sides, noting both the strength and weakness of Irish resistance to Norse invaders as well as describing St Bernard's views on Irish moral behaviour.
However, there are some potential biases that should be noted. For example, while it does provide an overview of Anglo-Norman rule in Ireland, it does not explore any potential negative impacts this may have had on Irish society or culture. Additionally, while it does mention Giraldus Cambrensis' account of conquest, it does not provide any counterarguments or alternative perspectives to this narrative which could be explored further. Finally, while it does note Pope Adrian IV's encouragement for Henry II's invasion, it fails to mention any other religious figures who may have opposed this decision or provided alternative solutions to resolving conflicts between Irish kings without resorting to foreign intervention.