If I want to make chord progression in A Major scale. Should I use the A, B, C#, D, E, F#, G#, A notes only?
You can write chord progressions using only chords with notes from the A Major scale. These chords are called diatonic to A Major. The triads diatonic to A Major are:
AMaj, Bmin, C♯min, DMaj, EMaj, F♯min, G♯dim
The seventh chords diatonic to A Major are:
AMaj7, Bmin7, C♯min7, DMaj7, E7, F♯min7, G♯min7(♭5)
The chord G♯dim (also written as G♯°) is a diminished chord, while G♯min7(♭5) is called a half-diminished chord, often written alternatively as G♯∅.
There are many ways to introduce non-diatonic chords into a progression (these are sometimes called chromatic chords). One simple technique involves changing a minor chord to a major chord. For example, the common diatonic progression
I7 - vi7 - ii7 - V7 in A Major: AMaj7 - F♯min7 - Bmin7 - E7 is often changed to AMaj7 - F♯7 - Bmin7 - E7. Here, the F♯7 contains an A♯, which is not in the A Major scale, so this chord is not diatonic to A Major. The second progression is not diatonic to A Major, but is still in the key of A Major.
The bottom line is that any chord can follow any other chord, if it sounds good. Not only is it fine to use notes outside of the A Major scale when writing in the key of A Major, but this is extremely common. Yet, if the goal is to write a strictly diatonic chord progression, then only the notes from the scale should be used.
By definition, yes! But that isn't what you're really asking I think. Songs 'in A major' routinely use plenty of chords outside the scale. Try the 'Get back' riff - A / |G D |A. Or 'Yesterday' A///|G#m7/C#7/|F#m/// etc. (not originally in A, but same difference). And that's just a couple of classics!