Anna's mother is from China, however, she can't speak Chinese.

Luke wants to study overseas, but he is afraid of living alone. (You could also use "however" here: Luke wants to study overseas, however, he is afraid of living alone.)

According to the rules, it's necessary for students to hand in their assignments on time. (This sentence is already correctly punctuated and grammatically sound.)

It isn't necessary for Cathy to buy new textbooks because she can borrow them from the library. (This sentence is also already correctly punctuated and grammatically sound.)

I have to be at school by 8:50 because the first lesson starts at 9:00.

Although Ann doesn't like sports, she has to play basketball in P.E. lessons.

I passed all my exams, so my parents were so delighted.

Tom is playing computer games right now, although he has an important test tomorrow morning.

Although she didn't get the first prize in the English Club, she is happy with the result. (Or: She is happy with the result, although she didn't get the first prize in the English Club.)

Because Jenny got up late, she didn't get to school on time. (Or: Jenny didn't get to school on time because she got up late.)