"Anna your brother does not answer me!"
Translation:Ana, fratele tău nu-mi răspunde!
It's redundant. You can use "mie" for emphasis, for example "he doesn't answer me, but he answers her" "Nu imi răspunde mie, dar ii răspunde ei" Usually, "mie" isn't used in this case since it's already implied that you're talking by yourself in "imi" Romanian is a funny language, you can say something in a lot of different ways
I haven't check the explanation very good, but it seems that you can make a kind of 'Liaison' as in french. If you see 'nu îmi' you can notice de letter 'î' practically does not have sound and is a vowel, and in the shortened sentence where is 'nu-mi' you just take off the vowel. Anyways, if you are working from a computer or tablet, on your top left side is the buttom 'Tips & Notes' or if you are working from a smartphone, in the main screen of the Dative Pronouns bubble is a detailed explanation about it.