The notes and positions for A-sharp are exactly the same as for B-flat.
3,1,4,3,1,4,3,4,1,3,4,1,3
For the B flat scale which is the most common for beginners: 1 6 4 3 1 4 2 1
Slide positions for a B-flat major scale.
The B-flat major scale for trombone consists of the following positions: 1st position (B♭), 4th position (C), 1st position (D), 4th position (E♭), 1st position (F), 4th position (G), and 2nd position (A). The notes in the scale are B♭, C, D, E♭, F, G, and A, returning to B♭. Trombone players typically use these positions to achieve the correct pitches while playing the scale.
Slide positions for B-flat tenor trombone concert pitch to middle C: C (6th), D(4th), E(2nd), F(1st), G(4th), A(2nd), B(4th), middle C (3rd)
A sharp is effectively a B flat, which is first position on a B flat trombone whether it is low or high.
To play "Amazing Grace" on trombone in the B-flat scale, start by familiarizing yourself with the B-flat major scale notes: B, C#, D, E, F#, G#, and A. The melody primarily revolves around these notes, so you can play the song by following the sheet music or a simple melody guide. Focus on smooth transitions between notes and use proper slide positions for accurate pitch. Practice slowly to ensure clarity and expression as you play through the song.
1, 6, 4, 3, 1, 4, 2, 1 (thats going from low Bb to high Bb)
Your either talking about the tuning slide, or the slide. The slide is used to play different notes, just like valves are used on trumpets. There are 7 slide positions, and different slides positions mean different notes. The tuning slide is used to make sure your in tune. If your flat (your pitch is low) then you push in on the tuning slide. If your sharp (your pitch is high) then you push out your tuning slide.
All brass instruments (except the sousaphone) have slides. They are used to adjust the pitch, sharp of flat. The instrument that is played using a slide is the Trombone. It also has a slide on the back that is used to tune, or adjust pitch.
F flat is simple an E scale. You didn't specify so I will give you both major and minor scales with notes and positions in parentheses The formula for a major scale is wwhwwwh so the E(Fb) major scale would be E(2)-F#(5)-G#(3)-A(2)-B(4)-C#(2)-D#(3)-E(2) On my trombone, the B is usually in a #4 and the High E is also a tad sharp. The [Musical]Minor scale in E(Fb) would contain the following notes E(2)-F#(5)-G(4)-A(2)-B(1)-C(3)-D(1)-E(2). If you need help in these, just remember your formulas. The slide positions are chromatic(half step intervals). That should help you if you need to think of them on the fly.