Expressions like "this week", "today", "this month" are a bit tricky when you need to choose between past simple and present perfect because the action is past but the time period is not over yet and without the context both are possible.
I saw John this week and he said...
Here you are talking about that particular time you met John and about what happened then. There is no reason to use the perfect tense.
I've seen John three times this week, I seem to run into him everywhere I go.
This implies "so far this week", which means that it might happen again.
Of course, you can say
I saw John three times this week.
That implies that you are quite sure you won't be seeing him again till the end of the week, for example it is already Sunday evening or you don't plan to leave the house or you have left the town where John is. Either way, those meetings are a past event.
The question and the negative are in the present perfect because they imply "so far, until now". You can also say
Did you see Bill this week? You were supposed to meet him on Thursday.
In this case we are talking about a particular occasion in the past and the past simple is more appropriate.