Please do your best to ...这样子说礼不礼貌?对方先写的we will do our best to ...是关于帮助我的,我该怎么回啊?不能光Thank you.想写Please do your best to ...因为要强调to 后面的内容就是不知道这么写是否太不礼貌?please let me know as soon as your work is(has been) done.I look forward to hearing good news from you.可否？

确实不妥，可以用I would be very appreciate that I can hear the news as soon as possible.

Thanks, looking forward to your good news.
谢谢，期盼好消息。

的确不礼貌.不要这样直接地说,你可以说那件事对你很重要,希望他们能尽快帮你处理好.比如：I really appreciate your efforts for.But as you may konw,this thing is very important to me.So I am looking forward ...