1. I fly back and forth from Beijing to Hong Kong every month 我每个月都乘飞机往返于北京和香港之间。 我每个月都乘飞机在北京和香港之间来回奔波。 2. I go back and forth to school and home. 我往返于家和学校之间。 3. She anxiously walks back and forth in her room waiting for the news. 她焦虑地在房间里走来走去，等待着消息。 back and forth：反复（反反复复）地、来回（来来回回）地 These are the basic translation of "back and forth", it may be strange if you use them directly. So you just need to remember the translation of this phrase iconically.

每个月我往返于香港和北京； 学校和家之间两点一线； 在家等消息时她紧张的来回的走

For no. 1, did you mean to say that you fly from Beijing to Hongkong and back again once every month? If so, it'd be 我每个月都会从北京到香港打来回儿。 Here, 打来回儿 means to do a return trip. If you mean to say that you make several trips a month, then say 打几个来回儿 instead, i.e. add 几个 ("a few") in front of 来回儿 to say that there are a few return trips being made. For no. 2, I don't think that the sentence makes sense in English either. Are you saying that "I'm always going back and forth between my school and my home every day"? To suggest the ennui of the student in this statement, I'd say 我每天就是在学校和家里之间打圈圈的。 Here, 打圈圈 means going around in circles. I'd use 家里 instead of just 家, so that the number of syllables matches up with 学校. No. 3 would be: 她一边在等消息，一边在她房间里焦虑地走来走去。 "While she's waiting for the news, she paces back and forth anxiously in her room" This construction uses "一边..., 一边...", which is like the "while" construction in English.

1,我每月在香港和北京之间来回很多次！ 2，我往返于学校和家之间！ 3，她在屋子里焦虑的走来走去！