“你的邮件我已经看到”“如有任何进展我会及时通知你” 请帮忙翻译成英文？？？

可以用被动语态“Your post has been received.”
也可以用主动语态“I have received your mail.”

“I'll tell/inform you(let you know) immediately if it works/moves.”口语化

有进展还可以短语表示：
make headway
make progress
get along
get around
(最好根据语境翻译)

你的邮件我已经看到”“如有任何进展我会及时通知你
I have read your mail,and I will inform you of any progress in time.

I acknowledge your mail

you will be informed when it makes any headway

YOUR MAIL HAS BEEN RECEIVED

WE WILL INFORM YOU AS SOON AS MAKE ANY PROGRESS

your mail have beed read.if there is any movement i will let you know at the first time(in time)