Learn English – Did you think you …. me somewhere before

The simple past, as in "I saw her" or "Did you see her?", generally implies a specific time, or inside a specific time-range that ends before the present. For example, I might say, "I was looking for her all of yesterday, but I didn't see her." This means that I didn't see her yesterday — but it doesn't say anything about whether I've seen her today. The following sentence could easily be, "So I guess she must have left town; I don't know if I'll ever see her again", or it could just as easily be, "But then I ran into her five times today, when it was already too late to invite her."

By contrast, the present perfect, as in "I've seen her" or "Have you seen her?", implies that the time-range of interest ends at the present. For example, one might say "I've been looking for her all day, but I haven't seen her."

It is possible to have two sentences that are identical except for this distinction, in which case the verb form conveys an important nuance of meaning. "I didn't see her today" implies that "today" has finished in some way — perhaps she is a coworker, and what I mean is that I didn't see her at work today, even if it's possible that I might run into her at the grocery store in the evening — whereas "I haven't seen her today" implies that there's still a chance that I will see her later today.

In your example, however, I would say that only "I'm looking for Paula. Have you seen her?" is acceptable. I cannot think of a context where "I'm looking for Paula. Did you see her?" would make sense. "Did you see her?" implies that you are referring to some specific past time or some specific past time-range; but since it doesn't explicitly indicate the time-range, that must be inferred from context. The problem is that the previous sentence, "I'm looking for Paula", implies that the time-range of interest is now, and the "did" version must end before now, so it's not compatible. As a result, saying "I'm looking for Paula. Did you see her?" makes about as much sense as "I'm looking for her. Have you seen him?" — the second part must be referring back to something, but it clearly can't be referring back to the first part, so the whole thing comes out sounding like gibberish.

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.