1. Can I cash a cheque here?
我能不能在这儿兑支票？
还能这样说：
Do you deal with the business of cashing a check?
Could you tell me if I can cash a check here?
应用解析：
a blank cheque 空白支票；自由行动的权力；
give sb. a blank cheque 给予某人全权，让某人便宜行事；
raise a cheque 增改支票上金额
2. How do I open a checking account?
怎样开个支票户头？
还能这样说：
What is the procedure for opening a checking account?
What should I do to open a checking account?
应用解析：
leave oneself wide open 使自己暴露在攻击之下；
leave open 未解决；悬而未决；
throw open 突然打开；取消对……的限制；
open with 以……开始
3. I want to change my traveler's cheque.
我想兑换我的旅行支票。
还能这样说：
I'd like to check out the traveler's cheque.
I want to cash this traveler's check.
应用解析：
travel around the world 周游世界；
travel to Hangzhou 到杭州去旅行；
travel over 眼睛仔细地看，逐个地看；仔细考虑
4. Do you charge for cheques?
兑换支票你们收手续费吗？
还能这样说：
Will you please tell me whether you charge for cheques?
Should I pay for the fee for cashing cheques?