Not sure which I qualify as on this one (MA in general, 14 years...current system, 5 months), so I'll play with all the questions
When learning a new form how often do you practice it?
Depending on how long the form is, it usually takes me 3-5 times through it in class to "get it" (I have the basic movements and understand it, now time to sharpen and strengthen it.) After that, I drive my roommates crazy by coming back to my place and going over it at least as many times that same night. I try to go over new forms at least 3-5 times each day while they're still "new" (unfortunately, time constraints make it go down to about once a day after that...otherwise I'd love to keep it up!)
How often do you walk through it each day in your mind?
Oh heavens, I can't even imagine. My most notable example is after learning my bo kata...I put myself to sleep that night going over it in my mind, and was thinking about it in the shower the next morning, and I don't think I ever fully stopped thinking about it for the next few weeks ^_^ The kata I learned recently is much longer than the bo kata, so most of the time I'll have a random portion of it pop into my head, then I find myself going over it!
How often to you picture opponents when you do the form?
Not often, unless I intentionally think about it. When learning it, I try to learn the application and understand the situation...aspects of that come to me during practice (for instance, every time I do a spinning hook kick during my kata, I picture where the opponent is so that I know where the kick is headed.)
How often do you see different techniques or applications of the given move?
I see these more often when thinking about the kata than when doing it...I love coming up with applications/tie-ins for moves though, so I think if I let myself see them while practicing it would become a problem & a distraction

lol
What do you concentrate most on when doing the form: movement, the technique, just remembering what to do next?
Initially, I focus on technique (to make sure I'm doing it correctly) and making sure I know what comes next (because, though I have a paper curriculum that describes the kata, it's very difficult for me to keep things straight if I don't remember it from my instructor.) After I have that down, I focus on strengthening the moves and improving my technique, as well as the little finesse details that make it a truly good kata ^_^
~Ani