But why can't a bishop from d1 move to A4 and what am I still overlooking here?
It can; the discussion was whether a bishop can move from e8 could move onto both of a4 and A4, whereas it ought only to be able to move to A4; from f8 it could instead move to a4 but notA4`.
Should the description consider the following knight moves?
Knight on b3, is the move to a5 possible, because on the same diagonal? Or a knight on a3, are the moves to a5 or b5 possible, because on the same line?
That depends on the definition of the Knight move: by the subtractive definition you and Fergus have used, those would be disallowed as a Queen could move to those spaces, as you've noted. Other definitions (such as the traditional ‘one orthogonal step then one step diagonally outward (or vice versa)’) would include those squares.
Which definition you prefer is in this case up to you
It can; the discussion was whether a bishop can move from
e8could move onto both ofa4andA4, whereas it ought only to be able to move toA4; fromf8it could instead move toa4 but notA4`.That depends on the definition of the Knight move: by the subtractive definition you and Fergus have used, those would be disallowed as a Queen could move to those spaces, as you've noted. Other definitions (such as the traditional ‘one orthogonal step then one step diagonally outward (or vice versa)’) would include those squares.
Which definition you prefer is in this case up to you