Is it possible to set time limit for the whole survey?

I know there is option to set time limit for some question types. I need to set a limit for the whole survey. If the user do not complete the survey within the time limit, the survey expires.

There is no "out-of-the-box" solution for this.

You would need to use JavaScript to create a cookie and keep track of the elapsed time and then, perhaps, use a solution like this to submit the survey - www.limesurvey.org/en/forum/can-i-do-thi...-or-go-to-end#121141

I'm not sure how well it would work with mandatory questions.

Is there a way to add custom fields to the survey settings. For example, to enter the time limit for the survey in this case.

No, that would require modifications to the core code.