Equalizing a temporal sound signal with a convolution
First, as long as your filter FFT has hermitian symmetry, the convolution with a real signal should also be real.  You may get some residual noise in the imaginary, but you can just pitch it.  If you are getting signal in the imaginary, your implementation is goofed.

Second, what you see is correct.  Because the time signal is real, the frequency signal has symmetry.  The opposite is also true.  Sample zero is the point about which the symmetry occurs.

Third, you have two lengths to take into account.  The sample window, N, and the filter kernel, M.  The sample window will determine how much real time lag you get through the operation, but is inconsequential in rendered applications.  The kernel length determines the number of “taps” in the filter bank.  The padding should be such that each signal is M+N-1 long when the operation is performed.

Fourth, this implementation is flawed because you are directly manipulating the signal in the frequency domain.  What you would want to do is something like this:  every N samples get M samples of the signal.  Perform an FFT.  Do whatever you need to to calculate the filter frequency response.  Set the phase to be linear and centered about the mid point.  Calculate the inverse FFT to get the filter kernel in the time domain.  Covolve the signals (w/ FFT convolution or directly).

Lastly, as I stated in response to your last question, this is not a good implementation of an analog prototype.  Analog filters have poles and should be implemented using biquad filters.  See RBJs biquad filter cookbook for a great source on implementing analog prototypes of common audio filters.  You can still do it the way I’ve described, but to relate it to the analog domain is a misnomer.