I’ve never heard of that fingering for F#. The standard would be to use 1 2 3 on the left hand, and either 2 or 3 on the right with pinky. That sounds more like an odd alternate fingering, unless I’m just reading your numbers wrong.

As for the Bb, definitely play around with using different fingerings depending on the situation. For instance, I love using the lever Bb in my chromatic scale, but if I’m playing a piece where almost every B is a Bb, I’ll use the smaller thumb key on the left and 1 on the left hand, pink on the right. You should be proficient in using any of these variations of fingerings though, so be sure to practice technique with all of them.