Equalization knowing the Channel State Information
To 1.
From the channel impulse response you can build the channel matrix and then compute the ZF equalizer coefficients using the pseudo inverse of the channel matrix.

Once you have the ZF coefficients you can convolve them with the received signal. 

To 2.
I guess you are referring here to a PNC system. The best solution is to use OFDM to solve this problem. In this case, you can use Maximum Likelihood detection per subcarrier by checking which combination minimises the Euclidean distance.

To 3.
You can find the equations for ZF equalizer in the book by J. Kurzweil, An Introduction to Digital Communications, 1st Edition.

BTW, the performance of the time-domain ZF equalizer is not very good in frequency selective channels. You are better off with the decision feedback
equalizer.