Does a diatonic scale contain more than 7 pitches?

A scale is defined by two tetrachords or with other words: by the tones between one octave, whereby the octave of the root (8 => 1) is identified as the same pitch class, and the scale remains the same 9 = 2, 10 = 3 etc.

Your example is in fact A natural minor. There are other minor scales with slightly different notes - but still called 'A minor'.

It matters not which notes you play - they are all actually the white keys on a piano - any (all) of them belong to A minor. You may have trouble singing a song with A4, B7 and C3 - those are big jumps in pitch!

If you start at the lowest white key and play every white key in turn, you have played a seven-and-a-bit octave A natural minor scale, ascending. Most people would play a two or three octave scale, starting somewhere near the middle , say A3 or A4.

You're talking about the difference between pitch and pitch class.

Pitch class is a pitch and all its octaves, like C1, C2, C3...

A diatonic scale contains 7 pitch classes. Usually people skip the term classes, because it's understood in context. Theoretically a scale has infinite pitches.

A scale can be continued in both directions as far as you want.