How should I finger A# and F# Major with the left hand, 5-2-1 or 5-3-1?
You should be able to lay all major/minor chords in first inversion as 5-3-1 (or 1-3-5 in the right hand). In most cases, F# Major included, doing anything else will generally cramp your fingers and make it harder to play.
The A# one could alternatively be played 4-2-1. This might help if you're having trouble stretching with your pinky to the black key.