Pumpernickel

If this chord progression is used, will there have been a modulation, unless the seventh of the I is preceded by a the diatonic seventh scale degree of the key?

What function does an augmented triad as in E, Ab, C, have? Where does it or can it resolve? What does it follow? Can it be used for modulation (and i don't mean augmented sixth).

So we can embellish the chords that secondary dominants tonicize in either their key or the key of the real tonic.

Yes but when you revert back to the original key from the secondary one, do you use the same sort of modulation as was necessary to get to the secondary key? Or do you just do it? And since you establish a secondary key I guess you embellish it as if it was in that key? Also diminished ninths = diminished and half diminished?

I have a question about secondary dominants, If you use a secondary dominant like V/V, but before it, use a chord that is common to both the original key and they key that the secondary dominant tonicizes, for example, I - V/V- V, In common practice do you automatically modulate to the key that the secondary dominant would be the dominant in? So if the example I gave was in C major, could you still continue in C major even after this progression or does common practice have you modulate to G major?