The Asturians and Galicians are Celtic peoples, but their Celtic languages are long lost (the modern Asturiano and Gallego languages are Romance languages, more similar to Portuguese than to Castillian Spanish as you mentioned. Asturia was the one Spanish region that was never conquered by the Moors, and only a small part of Galicia became part of the Moorish Kingdom; the Reconquista spread out from Asturia and Asturian surnames (with patronyms ending in “ez”) became the most common throughout Spain as the Moors were kicked out.
As for the Basques, if scientists discover that they emigrated to northern Iberia from another solar system, it wouldn’t surprise anyone.
I think in terms of genetic studies the Basques are the same as their surrounding neighbors
“end in -ez” — hmmm... I didn’t know that. But then how come the Portuguese version of such patronyms end in -es? Like Fernandes in Portuguese (which is related to Galician) is FernandeZ in Spanish or HernandeZ?