I will send you a fax with further details. --*Correct sentence~ ^^ 

It might be better you live in lodging at first before you make a contract a main house in overseas.

Better say: It may be preferable to live in lodging for a while before committing to a main property in another country.

Think about it's like a test choosing a correct words.

Better say: Consider it a test in which you must choose the correct words.

Our department has a daily meeting after the company was founded. -*Correct sentence~ ^^ 

Are there any available laptops you can borrow? *Correct sentence~ ^^ 

You should let me know a passwords and I can connect to your Wi-Fi.

Better say: You should provide me with a password so that I can connect to your Wi-Fi.

I haven't seen this last name before. -*Correct sentence~ ^^ 

Considering the context, I believe you have to apologize to your boyfriend. -*Correct sentence~ ^^ 

Can we check in before 12 am?  -*Correct sentence~ ^^ 

You can find ATMs easily everywhere near this place.  -*Correct sentence~ ^^