So, an arpeggio is a broken chord which is basically the notes of the chord played separately. That means that yes you can only play the F arpeggio or a substitution of F over the F (Dm7, Dm9 for example would also work). You can also play extended arpeggios(G6, Fmaj7, Fmaj9 etc), same holds for Am but instead of F transpose it all to Am.I get that but say I'm in F , you have F G A A# C D E . So if im playing in F then switch to A then to G can I only play the arpeggios or scales in A over A or can I play the ones in F over all of em?
I suppose you mean Am because A isn't in the F major chord family. Basically, for the scales you can use any scale that works over each individual chord. If you're progression goes from F to Am and you're in the key of F you can use F major over both of them, F lydian over both of them too, for spice you could even use F lydian#2 for example. In the general sense each chord has a set of scales that works over them and you're encouraged to explore what sounds good to your ear out of these options.
Hope this helps