Advice on setting up a real-time audio equaliser
Somewhat possible if you accept that the Arduino won't be doing most of the work:


Yes, the Arduino can sample audio and perform FFT on it, though not fast and not at high frequencies
Yes, the Arduino can decide what to do depending on the power of different buckets
Yes, the Arduino can display the results
No, the Arduino cannot do realtime audio filtering.


If you accept that the filtering will have to be done with a bank of analogue band-cut filters that the Arduino turns on and off as needed then it may be possible.

The Arduino Due might be a more suitable candidate since it will be able to sample and do the FFT much faster so you'll be able to respond to the peaks much quicker, and the displaying won't get in the way so much, but actively filtering inside the chip really requires a DSP.