In what respect does American fingering differ from foreign fingering, and which offers the greater advantages?

There is no "American" fingering. Many years ago the "English" fingering (which counts only four fingers and a thumb, and indicates the latter by a plus mark: +) was adopted by a few of the less prominent publishers in America; but it was soon abandoned. If you have a piece of sheet music with English fingering you may be certain that it is not of a recent edition, and I would advise you to obtain a more modern one. The advantage of the universal fingering lies in its greater simplicity, and in the circumstance that it is universally adopted.

The C-Scale Fingering for All Scales?

Do you advise the use of the C-scale fingering for all the scales? Is it practicable?

The C-scale fingering is not applicable to scales reposing on black keys because it creates unnecessary difficulties, the mastering of which would be a matter rather of mere sport than of art.

Fingering the Chromatic Scale

Which fingering of the chromatic scale the is most conducive to speed and accuracy?

The right thumb always upon E and B, the left one upon F and C. Between times use three or four consecutive fingers as often as convenient. At the beginning of a long chromatic scale select such fingers as will most naturally bring you to one of the stations just mentioned.

The Fingers Needed to Play a Mordent

When executing the mordent, is not the use of three fingers preferable to two?