“All those are natural born subjects, whose parents, at the time of their birth, were under the actual obedience of our king, and whose place of birth was within his dominions.”
Aliens, living in the country, were under obedience to the king. Blackstone discusses it. So if aliens had kids while in the UK, they were under the obedience and their kids were born in country - and thus the kids were natural born subjects.
That statement is in complete agreement with the discussion in WKA. So your reference agrees with Blackstone, WKA and me.
No. You're reading into it what you want it to mean.
Children born in England to aliens could NOT inherit property, holdings, etc., from their parents. Children born in England to English subject parents could. So while Blackstone may choose to say that "children of aliens, born here in England, are, generally speaking, natural-born subjects, and entitled to all the privileges of such," the fact remains that there indeed were significant differences in the rights and privileges of each. That's why Blackstone deliberately uses the disclaimer, "generally speaking." He knows they were not the same, as should you.