Yes, English law not U.S. Law. For clarity you can look at the case of U.S. President Chester Alan Arthur.
What is the source and circumstances of the quote you referenced?
http://www.law.cornell.edu/supct/html/historics/USSC_CR_0169_0649_ZO.html
English law not U.S. Law.
Nope.
"III. The same rule was in force ... in the United States afterwards, and continued to prevail under the Constitution..."
As I said, if you don't like it, go argue with the Court. I consider a Court ruling a good deal more authoritative than special pleading by cherry picking ancient authors.
I am unaware of any legal decision involving Arthur's situation. Claims were made he wasn't NBC. But it appears the claims never got any traction. Nobody cared.