I don't care vs. I don't mind

Great job! There are no grammatical errors in these dialogues you created. They also show that you seem to understand the difference between the two expressions. They are very similar and can often be interchanged, but "I don't care" means you are indifferent (you have no feelings about the matter) whereas "I don't mind" means you are okay with the situation, you accept it. Sometimes "I don't care" can seem rude because people may think you mean that you don't care about them.

I was confused by the two expressions and I made dialogues by using them.

#1 - I don't care
A : Why don't we go to the movies tomorrow? I like action movies!

B : Sorry, I'm very busy (or My schedule is full). I don't care whether you like it or not. Excellent! Both "I'm very busy" and "My schedule is full" are correct.

#2 - I don't mind
A : Would you mind closing the window (or Would you mind if I close the window)? Perfect! Both are correct. "Would you mind closing the window?" means you are asking the other person to be the one to close it, "Would you mind if I close the window?" means that you will be the one to physically close it.

B : No, not at all. Go ahead.