Hello Andrea,
Will the timer be reset or stopped and resumed, Will it go on?
The timer is on the server. Therefore, it continues to run no matter what happens on the student side.
You can change the time limits for a particular user (or for a group of users) by clicking on the name of the quiz / gear icon / User overrides / Add user override / select a student and set the new time limits (similarly for Group overrides).
And when student will manage to log in again what will happen to answers. Will they be still there for him? Will he have to start anew again?
The student can continue his/her attempt even if he/she had problems with the Internet, there was a power failure, or left Moodle and temporarily shut down his/her computer for any reason.
When the student resumes his/her attempt, he/she will find all the answers that have been saved and he/she can simply continue as if nothing had happened. answers that have been saved means the answers for which the "Check" button was last clicked.
If an answer is entered but the "Check" button is not clicked, that answer will be lost.
Note that there are two cases where there is no "Check" button: the "Essay" question, and all question types (True or False, Multiple choice, Calculated, etc.) if "How questions behave" is set to "Deferred feedback". In these cases, students can save
their work by clicking on "Finish attempt" and then immediately clicking on the "Return to attempt" button.
In all case, make sure students understand that if they click "Finish attempt" and then "Submit all and finish" twice (the second time for confirmation), they will not be able to resume their attempt.
There may be students for whom you want to give a second attempt for special reasons. In this case, click on the name of the quiz / gear icon / User overrides / Add user override / select a student and set "Attempt allowed" to 2. You must also set "Grading
method" under "Grade" and "Each attempt builds on the last" under "Question behaviour", in the quiz settings, according to what you want for these second attempts.
You can do tests on the Moodle sandbox and Activity examples where you can log in as a teacher and as a student.