Learn English – Present Continuous with state verb “see”

We use the present continuous for actions taking place now, at the moment of speaking. So, when you have to describe what somebody is doing right now, you don't have to start thinking when she put on her hat, or if she has just sat down. What is she doing now? She's sitting and wearing a hat.

If this is from an exam or class exercise you may point out to your teacher that any of the options may be correct.

I haven't seen Kumar this week. —As you say, this speaks to the current state of things: it says that you haven't seen Kumar during the part of this week that has already passed, but it leaves open the possibility that you may see Kumar during the part of the week that remains.

I didn't see Kumar this week. —You would use this if the opportunity for seeing Kumar this week has now passed: for instance, if you ordinarily see Kumar on Tuesdays, you might say this later in the week if one of you was otherwise engaged at the time of your usual meeeting.

I am not seeing Kumar this week. —You would use this if an expected meeting with Kumar will not after all take place. For instance, if on Tuesday someone asks you to bring up an urgent matter with Kumar at your regular Thursday meeting, but you know that Kumar is out of town this week, you might say this.