The date of Arvedui's birth appears only in The History of Middle-earth volume XII, The Peoples of Middle-earth. It cannot therefore be considered completely reliable.
2
The Appendices to The Lord of the Rings are apparently ambiguous on the date of Arvedui's death. Appendix A gives it as III 1974, the same year Arvedui's kingdom fell, but the Tale of Years in Appendix B gives the following year, III 1975.
Fortunately, the fuller story of Arvedui's defeat in Appendix A has enough detail to solve the mystery. The invasion of Arthedain took place in III 1974 'before winter was ended' (which can only mean very early in the year). The ship sent to rescue Arvedui only arrived 'after many days', and when it reached him 'it was then March'. So, this places all the action - including Arvedui's death aboard the stricken ship - during the first few months of the year III 1974.
In the original form of the story, found in volume XII of The History of Middle-earth, the rescuing ship did not reach Arvedui for an entire year. That's the reason the uncorrected Tale of Years gives III 1975 for the date of Arvedui's death.
3
It may seem strange that Arvedui was named 'last king' from the time of his birth, but there is an explanation for this. He was named by the famous seer, Malbeth, who foresaw that either his kingdom would be ruined, or Arvedui would reunite the Two Kingdoms of the Dúnedain. Either turn of events would see Arvedui as the last King of Arthedain - in the event, the kingdom was destroyed and Arvedui drowned in the cold northern seas.