Only if the clarinet is a D sopranino clarinet. If it's a standard B-flat soprano clarinet, then C major for it is B-flat major on the piano. If it's the slightly less standard A soprano clarinet, then C major for it is A major on the piano.
There is an infinate ways to modulate from C major to D major.One way in which you can do this is use a "pivot chord" which is a chord that is similar in both keys. The chords similar between these...
Throughout the whole keyboard, there are a few sets of "A's" and "C's" and so on. If you are starting from middle C and then the A above it, obviously A is higher. If you are starting from middle C...
If you played a root position chord on each note of the C Major scale, including all the notes in the scale, all the chords would be made up of white keys. Starting on C... C-E-G, D-F-A, E-G-B,...