Yep, both are OK. :) "I'm happy for your improvement" is a little more formal and distant, as it doesn't talk about the person, but instead their progress. You could really hate the person but still say this sincerely. "I'm happy you have improved" is about the person, this is much more friendly and is more of a compliment.

Both are correct. Although usually when people say "I'm happy for you," there's an undertone of, if not bitterness, then a soft resentment. Like when woman X has been dying to get a child, but can't, and her best friend Y gets one, she might say: "Well, I'm really happy for you." Doesn't mean she's lying; just means exactly that: she's happy for her, but not overall happy with it for herself (in this case, because she wants one herself too). So, I would go with "I'm happy you have improved." It sounds a lot more natural, and doesn't come with notion that you're detracting something from said happiness (like "I'm happy for you" does).

Actually, come to think of it, consider also this one: "I'm pleased with your progress." Which is what a teacher, or your boss, might say to you. They wouldn't be inclined to say "happy" (as it's more personal); rather, they want to express that they're satisfied with your progress. And 'progress' is actually prefered over 'improvements' here. You either 'have improved' or you 'made progress.' But "I'm happy for your improvement," while not strictly wrong, really sounds just a mite off.