Acts 1:19, continued: Why is the NT word for 'Jerusalem' sometimes feminine singular and sometimes neuter plural?

Let's begin with our conclusion: it's just one of those language things.

Various koine Greek sites have included discussions on this point (see, for example, here and here; there are others).  What seems to be clear is that yes, there are two forms of the Greek transliteration of the Hebrew word for Jerusalem.

One is always feminine, singular, and indeclinable, i.e., as found in Acts 1:19, and spelled Ἱερουσαλήμ (note the rough breathing).

The second is always neuter, plural, and declined according to grammatical function.  In Mark 3:22, for example, we see the genitive plural form after the preposition ἀπό:

καὶ οἱ γραμματεῖς οἱ ἀπὸ Ἱεροσολύμων καταβάντες ἔλεγον

and the scribes (the ones) who had come down from Jerusalem were saying

The two forms are found in very approximately equal numbers in the New Testament.  There is discussion about possible nuances of meaning between the two, but I do not see a clear consensus.

Why would there be a feminine form for Jerusalem?  In Hebrew (as I understand it, and let the reader beware) cities are feminine; that is, their names are considered feminine proper nouns.  And in Greek, the word for 'city' itself is feminine: ἡ πόλη.

What about the neuter plural form?  For this, all I can say is that ancient Greek did have a number of plural-named cities, notably Athens - αἱ Ἀθῆνα - and Thebes - αἱ Θῆβαι.  However, these plurals are feminine.

It may very well be a tendency from Hebrew, but on that I am able to say no more.