I can't help for c), but both a) and b) appear to be correct. I treated it as a continous system, in which case, you have
This gives that . Treating September 2009 as your base gives A=21.5. Taking a time unit of one month gives , giving my r to be 0.1033.
Then, after 15 time steps, . I would assume the difference that we have between our answer is due to the number of decimal places or something similar.
Working in much the same way gives that the time step required to get 200 million SMS is 21.59 months. Again, I would ignore the minor difference between answers.
Your method is perfectly valid as well, just to note.