1. Each of them is doing his/her(their) work.

Should I use "his/her" or "their"?

2.Every of them .............

is such (2) is possible?I mean "every" can function as pronoun?

In more formal contexts, use "Each of them is doing his work."
In ordinary, everyday conversation, you can use "Each of them is doing their work" OR "Each of them is doing his work".

Every one of them ...
I would choose 'his or her.' for 1.

For 2, you can't use 'every' as a pronoun.
'Every of them...' is definitely incorrect.
 CalifJim's reply was promoted to an answer.