The questions are correct, and so are the answers. However, you can have the answers sound a little better, A: Is your sister working these days? B: No, she is not. She is just doing some housework. A: What about your brother? B: The first semester just started, so he is getting prepared to improve his grades. I hope this helps Khaled!

Here are some other alternatives. A: Is your sister working these days? B: No, she's not. She is staying home to care for the family. A: What about your brother? B: The first semester has just started, so his focus is on improving his grades.

It’s very understandable but the answers aren’t quite natural/correct. The questions are very good colloquial English. A good response for the first one would be “Not outside the house.” Which implies she does a lot of work around the house but not outside it. She’s just doing domestic work doesn’t sound as natural. She stays at home with the children or She takes care of the house is better, but my first option is most considerate. The second response is pretty good, just not how it would be said. “The first semester just started. He is studying a lot so he can get good grades.” The only reason I split the sentence was to avoid having “so” twice and sounding redundant. People do it all the time in informal speech though. Another option is “The first semester just started so he is studying a lot to get good grades.”