Is it a must to have a frequency ear training to accomplish a good mix? How long will it take for one to at least internalize the one octave increment? Thank you.

There are books and programs for ear training, but I've not tried them. One resource that keeps coming up is F. Alton Everest's Critical Listening Skills for the Audio Professional. I've been meaning to get that book for years. (The same author's Master Handbook of Acoustics is a standard reference that should be on everyone's bookshelf.) But I haven't, for the simple reason that ear training is something that happens naturally whether you actively pursue it or not. However, I'm sure that a formal training regimen would shorten the time needed versus natural osmosis, which takes years.
 
To answer the question directly, yes, ear training is absolutely critical. Without it you're stumbling in the dark, twisting knobs and hoping serendipity will save you.

it really helps.
 
having something like voxengo SPAN, or even Har Bal, helps you visualize what you are hearing..
so you can make that right brain - left brain connection.
 
 
how can you ever uncover masking issues, if you don't even know what typical frequencies, say, of a rhythm guitar and male vocal, where they cross over....?