Can I make any changes after I have selected my original stable of (12) twelve horses, verified it and made my initial (6) six horses active?
No. Once you make your original stable selections (12 horses), submit them, verify them, and activate six runners, you cannot go back and change any stable members. In short, those 12 horses will be in your stable for the duration of the game. You can, however, change your active horses as many times as you want on non-scoring race days.