Learn Italian: Ero sul punto di sussurrare la risposta. - I was about to whisper the answer.

Both expressions describe an action that is about to happen, but essere sul punto di is slightly stronger and more emphatic. It translates literally to "to be on the point of" or "to be on the verge of." It is perfect for highlighting the extreme imminence of the action, whereas stare per is the standard, everyday way to express "about to."

Why is essere in the imperfect tense (ero) instead of the passato prossimo (sono stato)?

The imperfect tense describes an ongoing state or background condition in the past. Because "being on the verge of" doing something is a continuous state that leads up to an action, you almost always use the imperfect (ero sul punto di). The passato prossimo would imply the state abruptly started and finished, which clashes with the meaning of an imminent, pending action.

Does the phrase essere sul punto di always require the preposition di before the next verb?

Yes. When linking this phrase to the action you are about to perform, you must use di followed by an infinitive verb (here, the present infinitive sussurrare). You cannot drop the di or replace it with another preposition like a or per.

I have also heard the verb bisbigliare. Could I use that instead of sussurrare here?