(Expanding on an earlier comment…)
Tunny’s answer is correct: “to expostulate” is the subject, it doesn’t seem to agree with “were” because this is an archaic form, and “is” is missing in a literary technique known as ellipsis. (Incidentally, this sort of ellipsis is literary but not archaic. Another famous example is Pope’s “To err is human; to forgive, [is] divine”.)
As for terms you might use to describe the first question, you could say that “were” is an example of an irrealis mood (that is, one used to talk about hypothetical or unreal situations) and that modern English uses the modal verb “would” instead.
As TRomano suggests, though, “irrealis” is a term that comes up more often in formal studies of linguistics than in English language learning! I hesitated before including it, but since you asked for terms I thought it was worth mentioning.
An alternative term for the “were” construction is the subjunctive, but not everyone uses that name. For instance, the Cambridge Grammar of the English Language reserves the term “subjunctive” for constructions like
I demand that he leave at once!
God save the Queen!
or (from the fairy tale of Jack and the Beanstalk)
Fee, fo, fie, fum
I smell the blood of an Englishman!
Be he alive or be he dead
I’ll grind his bones to make my bread!
(helpfully mentioning this on p. 50 which is freely available online in sample chapter 2). This usage is not quite archaic but certainly either rather formal/literary or part of set phrases like “God save the Queen”.
There was an interesting discussion on the Language Log blog (one of whose writers is a co-author of the Cambridge Grammar) a few years ago about this sort of “were” and what to call it.