Newguest“1. A famous artist painted Mark's portrait. I would say: Mark had his portrait painted by a famous artist, however, the key in my grammar book says: Mark is having his portrait painted by a famous artist. I suppose the answer in the key is wrong?”
You suppose correctly. You are right; the book is wrong.
Newguest “2. Some vandals have smashed two windows in my parents' house. I would say: My parents have had two windows smashed in their house. However, the answer in the key is: My parents had two windows smashed.. . Is my version correct?”
Your version is correct.
Newguest “3. Kate's sister did her hair for the wedding. I would say: Kate had her hair done by her sister. The key, however, says: Kate has her hair done by her sister. Why "has"? Is it another mistake?”
This is the same situation as in your other two examples. For some reason, the answer key is changing the tenses in the original to different tenses in the answer. Make them stop doing that!!!
Try rereading the instructions for the exercise. Did the instructions say anything about changing the tenses?
CJ