Reading the guide will answer your first question as well as the Item Guide regarding if a certain TM/Move Tutor is in the game or not.
But to answer your questions, the only way to get Ice Beam onto Milotic atm is through breeding by going to an Episode that had Gen V Breeding Mechanics, any episode before Episode 13.
And regarding breeding Brine, there really isn't a "best" one. If you want to see what mons can breed Brine onto Miltoic, look at this link: Milotic Egg Moves