gurjyot I need a closed website. Where only the employees can have login access and noone else can see anything.
Yes that's possible. Aside from making all discussions only visible to members and using doorman (or similar extension) to limit registration, you can also make things a bit nicer using the private facade extension.
gurjyot Employees in a particular department should not be able to see what tasks are given in other department.
You can limit who sees which tags by user group. That would be the simplest solution.
gurjyot Tasks can be assigned to an employee. (I think the mention feature should work here).
That feels like a hack. There's no better solution yet though.
gurjyot How to mark the tasks as completed?
You could use a Completed secondary tag, similar to how we use Solved.
What might be of interest to you is a Kanban kind of extension. I built one for Flarum during its betas. If interested I could potentially revive that as a premium extension.
The ability to assign discussions/cards to one or more people was actually planned, but due to a lack of interest never completed.
Edit: sorry I forgot the rest of the questions 🙂