Super, I win today my first reward 1000 hyperstake !!

My block of 20K is divided by 2, do I have to redo 1 block of 20K?
No. You haven't.
I would set setstakesplitthreshold to 20000 if you haven't done so far., which has the same effect you've just got. When a block hits 20K, it will split into to blocks which will begin to stage again and again gaining 1000 coins each time until they hit 20k and the process will start again. Obviously, with time, you'll have more and more blocks.
I have indeed this setstakesplitthreshold set to 20k with 64 blocks and works fine.
You can check your current stakesplitthreshold within the console with "getstakesplitthreshold".
I think that in case a block has reached the "max-age" possible, it won't break apart, but maybe someone can confirm this.