The pictures I've seen of the fragrans Massangeana don't match up. The trunk of this tree is maybe three inches and the leaves are about 36 inches coming up from the trunk, like a snake plant grows straight up.

Pilea microphylla, Artillery Plant. HTH Chris

That would be fine until frost, then it needs to come back inside. I don't know that I would take this Impatiens outside at this point. It's been fine for 4 years where it is, has sentimental value, and would be much more likely to catch downy mildew outside, a fatal (always/usually?) disease of I. walleriana. Snapping off the taller stems would result in more mass closer to the soil. When those are growing again (both the cut piece should continue to grow, along with new growth from the stump,) snap a few more. Doing it gradually would prevent the "bunch'a stumps" look of doing it all at once, and any risk associated with failure, though small. You could start a new pot or just make the current pot look more full. Since these plants do snap easily, repotting is difficult on one with many tall stems such as yours, I might opt for sticking cuttings in a pot of fresh soil. When a nice 2nd pot is going, a repotting attempt could be made on the mama plant without so much concern.

Looks like a plumeria. There is a whole forum on them here on gardenweb. It's probably not flowering because it wants better soil/bigger pot.