I see a problem right away in the way you are looking at the analysis. When you analyze something and notate either a chord or a Roman numeral the chord is meant to analyze all notes and pitches up to the next chord/Roman numeral change with the exception of a few non-harmonic tones that are typically notated. Also note you are in the key of C# minor so the notes F,C,G, and D are sharp unless otherwise noted.
- The notes in the first measure are two C# notes in the lower staff and G#,
C#, and E in the top staff. This does in fact make a C#m chord.
- The notes in the first half of measure 3 are two A notes in the lower staff and A,
C#, and E in the top staff. This does in fact make a A major chord.
- It is typical to speed up the harmonic rhythm as you approach cadences. At every place you mention there being more chords I see a cadence so this is a very typical and expected pattern. I wouldn't call any part of this syncopation because even though the chords are changing at a faster rate, they are still changing on predictable on the beat fashion even though it is sometimes the weak beat. In syncopation, there would be chord changes that are off-beat which is different.