a)—

Common law takes precedence over New York State Statute - it says so in a New York Statute. ;)
Unless there is a statute specifically eliminating a particuar common law,
such as common law marriage.
in the event that common law and statute conflict ...common law takes precedence over that statute.

b)—

Read about common law appearance being any action taken that would impede plaintiff from seeking judgment in the case.
Read a few case law snippets showing that obtaining an extension of time to answer is an appearance.

c)—

Read a simple statute mandating service of papers on atty.
Read a few case law snippets regarding failure to serve papers on atty.

d)—

Read simple statute about waiver of procedural due process by participation without raising it.
Read a few case law snippets regarding waiver if atty not noticed, unnoticed atty does not appear, unnoticed atty does not file/serve opposition papers.

e)—

Read a few case law snippets regarding:
absent waiver by participation*** w/o objecting to procedural due process violations
procedural due process violations vest no rights and
have no deadline (statute of limitations) to overturn.
***absent any participation that does not object to lack of procedural due process.
things such as attending hearing without raising issue or opposition papers without raising issue, none of which occurred here.

f)—

Scan docket and note lack of proof of service of anything on that atty.

g)—

Swear out a jurat (enhanced affidavit) in front of notary public attesting to some of these simple things.

h)—

Appear at a hearing either on zoom-like technology, or, in person
(not required but garner votes)

i)—

give us some relevant caselaw we don't yet have on concepts on or concept list Can be from any jurisdiction.
Can be for or against our positions.