I have tried transposing this piece of Amazing Grace. Did I get it? Thanks in advance.
C F A F A G F D C
D G B G B A G E D
E A (C#) A (C#) B A (F#) E
F (A#) D (A#) D C (A#) G F
G C E C E D C A G
A D (F#) D (F#) E D B A
B E (G#) E (G#) (F#) E (C#) B
For the melody notes you've posted for the first line in the lyrics of "Amazing Grace," you've almost got the transpositions correct for the various keys you used. I realize that in forming each successive transposition you posted, you simply adjusted each note in that sequence of melody notes by the step or half-step change you made in the first note in that sequence. That procedure is fine, but you must also use the correct note names, as found in the scale associated with the key to which the transposition is being made.
The first sequence of notes you posted is for that segment of the melody as written in the key of F-major, which has one flat, namely Bb, in its key signature. You then transposed that segment into the key of G-major, which has one sharp, namely F#, in its key signature. Well done!
Next, you transposed that segment into the key of A-major, which has three sharps, namely F#, C# & G#, in its key signature. In general, when writing out the sequence of melody notes, do not enclose flatted or sharped notes in parentheses. So the notes would be written as E, A, C#, A, C#, B, A, F# & E, in the key of A-major. Other than for the parentheses issue, your transposition is correct. Good work!
You then transposed that segment into the key of Bb-major, which has two flats, namely Bb & Eb, in its key signature. So the correct sequence of melody notes in that key would be F, Bb, D Bb, D, C, Bb, G & F. There is no A# (which is enharmonically identical to Bb) in the scale associated with the key of Bb-major, so it is technically incorrect to name that note A# instead of Bb when the melody line is written in that key.
The remaining three transpositions you worked out are correct, but should be listed without parentheses for any sharped notes. Congratulations!
Have you tried to transpose that same melody segment into the other primary/standard major keys --- Ab, B, Db, Eb, F# & Gb? Try to transpose from any one starting key, say the key of C-major, directly to each one of the keys I've listed here. Have fun!
Make mellifluous music!