shall i inform the lender about the completion date?

As far as I know it is your solicitor's job.

yep, but one paper to sign.

一般exchanged 之后多久才是completion呢?

Depends, usually it takes two weeks, while some can be done in one week.
Exchange day and completion day can be put in the same day, discuss it with your solicitor.

哦,谢谢
那通常订金是在exchange那天交,还是要提前交的呀?

May I ask what paper are you talking about, 小虫? Usually,your solicitor and vendor's solicitor should take care of all paper documents to be signed by both of you, you ought not to do it yourself.
Completion date should be passed to both of you by your solicitors as it's a formal means,however you can still inform the vendor infomally

exchange day. If i am not mistaken, your deposit has to be in your solicitor's account due to exchange day, bear in mind that it takes usually 3 working day for cheque clearing in the bank. keep tight contact with your solicitor and ask whatever questions you have, they are responsible for that since you pay for the service.

谢谢,这样有数了,知道怎么准备了.