Something can be uniform and fluctuating at the same time. All that's required is that the fluctuations follow the same, regular pattern everywhere. I have no idea whether this is true for the CMB, however.
It is true. Further, the fluctuations are tiny - at the parts per million level. It took 28 years after the CMB was discovered to detect any fluctations at all, requiring a sophisticated space probe (COBE) to do it.
Asserting that the CMB is "not uniform" because of these fluctuations is rather like saying the Bonneville Salt Flats are not really flat at all since the surface has millimeter scale irregularities, or your polished marble dining room floor isn't flat since it has micron sized irregularities.