The POD should go back to the Reconquista. The first alternative is Sancho III "the strong" in the XI century. If he does not divide his realm between his sons we would have an earlier Spain but formed from Navarre as he claimed the title of Rex Hispaniarum. Then in the XII you could make the personal union with Aragón under Alfonso I to survive, then we could have a kingdom of Navarre dominating the Ebro valley. You have the same posibility in the XIII century when Sancho VII declared his heir Jaime I of Aragon (and Jaime I declared his heir Sancho VII). Let Jaime I die and the aragonese noblemen to accept Sancho VII and you have another Aragon-Navarre union. Later than that it would be hard to imagine and Navarre would have to face annexation to Castille, Aragon, Spain or France.
As for the basque question, that would depend. If you have Castille integrated in Navarre, the answer is yes. If not, you must have into account that Castille was born as a way of defending the interests of basques and castillians against the strong kingdoms of Leon and Navarre. Whenever the basques incorporated freely to another political entity that was Castille.