From the genitive 'Delphōrum', it seems to belong to the second declension. But is it used as a singular or a plural?
It is indeed a second declension word. It is used in the plural. You can confirm this on the Lewis and Short dictionary:
I.the famous city of the oracle of Apollo in Phocis, now Kastri
Understandably, the word comes from Greek, being a Greek city and all. The Greek word, Δελφοί, is also used in the plural.
Thus, the Romans probably used the plural because the Greeks did themselves. This is true of many Greek cities. Ἀθῆναι > Athenae > Athens. Θῆβαι > Thebae > Thebes.