Peretz,
I do not know what it means to use "labview for DSP target (without CCS)". TI supports using CCS with our devices to load and debug the code. If you are using some other means, then we can only help with specific device-related questions.
Your questions about the 48KHz sample rate causing corruption usually are caused by overloading of the DSP such that real-time requirements are not met. But I am not sure that you have tested all the steps getting audio in and out of the DSP. That is, from your comments on analog to analog, then adding FFT, it sounds like there are a lot of test steps in between that you have not tried. Try just bringing in the digital audio and connecting the digital audio out to the digital audio in, with no other processing like FFTs.
You can look at the tutorials for GEL scripts to find how sliders are easily implemented in GEL scripts on TI devices.
Regards,
RandyP