When changing between the C and D7 chords the first finger does not move. The note played by the first finger (a C note) is common to both chords. The second and third fingers move to their new position and the first finger acts as a pivot. The use of pivot fingers will make chord changes easier.
Always hold the complete chord shape even though you do not play every string.
Fingerpicking Pattern 1
This is a sharp sign. It indicates that a note on the stave is played one fret higher. If you are not familiar with this symbol see Progressive Guitar Method: Book 1 .