Is it appropriate to sing Amazing Grace at a Jewish funeral?

Answer 1

Although aged 75, I have been spared the need to attend many funerals,
both because my family and community have been blessed with long life
in good health, and because I am a Cohen.

At the few Jewish funerals where I have been present, I have never heard any
singing at all, except for the chanting of the Kaddish.

With regard to the particular song that you mention, that one would be quite
inappropriate. Its origin and lyrics are steeped in the Christian tradition.

Answer 2

No. It is a Christian song, with overtones in that vein. See also:

Jewish mourning and burial customs