nōn modo quaerimus utrum… is an indirect question (we are not now asking whether…)
so the following two subordinate clauses must be in the subjunctive mood.
first subordinate clause
prefect passive construction
indicative: this was done (or this has been done) est factum
transform to subjunctive: est → sit (present indicative → present subjunctive)
sit factum
second subordinate clause
passive periphrastic construction
indicative: this was to be done (or was deserving of being done) fuit faciendum
transform to subjunctive: fuit → fuerit (perfect indicative → perfect subjunctive)
fuerit faciendum
Sequence of Tenses
Note that since quaerimus is a primary tense in the main clause, the subjunctive in the subordinate clause can only be present or perfect tense.
Many thanks katalogon for this very helpful analysis. I was thrashing about trying to recall the grammar terms to look up, but the sentence raised so many questions that I was overwhelmed.