Is there way to give extra time for submissions to one student?
By googling I found out that at least quiz has this feature, but at workshop I found only global "allow late submissions" option.
What that "Allow late submissions" feature does is
In your case, you could use the new Workshop capability introduced in Moodle 2.1 to ignore all deadlines. If a user is given such capability, none of submission-start, submission-end, assessment-start and assessment-end deadlines apply to them.
Upgraded to 2.1, seems to work.
But I don't quite understand... I am logged in as admin. I am at Home -> Cources -> [category] -> [course] -> Users -> Permissions. And there is "Ignore time restrictions", but what to click now?
Well, that's a pretty advanced feature of Moodle and it is not Workshop specific. You should definitely read something about roles, capabilities and permission overriding before you start experimenting with this. However, in short what you need to do is
To give a particular user the permission to ignore workshop deadlines, you must first decide whether they should have it at a course level (hence for all workshops in it) or in a particular workshop instance only.
OK, this works.
But then, when system has moved to Assessment phase, it is no longer possible to submit anything. It is of course logical ja simple arrangement. However, in real life, it is too restrictive. I will start new thread about this.
As you say, quiz has this feature. In fact it belongs to a more general feature of creating exceptions for certain students.
Quiz can do that because Tim Hunt (i believe) implemented it when refactoring the quiz code, but it's a feature pretty unknown to people, even between some Moodle developers. Hope one day it will be implemented across whole Moodle.