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if you see at the 5th measure from the photo, there is a question mark.
How did that F#7/A# came out all of a sudden ?
Was it possible because at the measure before there is a bass movement moving down from B ? so that makes it a half step movement ?
or is it just possible that Secondary Dominants could come out of nowhere all of a sudden ?
Yes, It's possible that secondary dominants can come out of the blue all of a sudden. While the chromatic bassline definitely supports those harmonies, I don't think it's necessary in order for those chords to be used.
In this case, the F#(7)/A# starts off a long chain of secondary dominants, so it sounds even stranger. Such long chains of secondary dominants aren't unheard of, though: see the ragtime progression for more details.
or is it just possible that Secondary Dominants could come out of nowhere all of a sudden ?
Yes, secondary dominants have this properties.
And mind the chord progression: measure 4 - 8, this is an entire cadence of secondary dominants following the circle of fifths. This progression is quite usual in all epoques and styles of music.
