Hello JustNix -

Yes - you can trim too long stems off. It will get bushier. You can stick 3-4 inch tip cuttings into the pot with soil and cover it with a baggie to keep humidity hi - they root fast and you can later put them all together with the mama plant.
Yes - it will benefit from repotting. The soil you can use is African Violet mix plus 1/3 perlite.

Are you fertilizng it? Weak solution of AV fertilizer or fish emulsion works miracles.

There are many-many hybrids and species with different habits. Some bloom once a year. some need cool temperature to stimulate the bloom setting. So -if you crack the window to let some cool air in - may be it will get it.

By the way - they like light - but in my experience - morning light is the best - and they do not get enough if the glass is tinted or has heavy e-coating. Something is missing in the light.

Good Luck

Irina