Yes it uses the whole tone scale as there are no semitones in the melody. You are right.

One difference between a whole tone scale and a pentatonic scale is that a whole tone scale has 6 notes per octave while a pentatonic scale has 5 notes per octave. Another major difference is that a whole tone scale has all adjacent notes a whole step apart, while a pentatonic scale does not consist entirely of whole steps, and since a pentatonic scale is only defined as a scale with 5 notes per octave, there are many pentatonic scales that are possible.

I'm not sure exactly what you mean by how many steps but I can explain a whole tone scale for you.

A whole tone scale is comprised of all whole steps. For example:

A B C# D# F G A

or

Bb C D E F# G# A# (which is Bb)

So I guess there are 7 notes in the whole tone scale if that was what you were looking for.

Whole-Tone Scale

It is a scale made up exclusively of whole steps, as distinct from the standard western diatonic scale that is built upon the structure whole-whole-half-whole-whole-whole-half. For example, starting at E flat, the notes of a whole tone scale would be E flat, F, G, A, B, D flat.