EGT became high after carb cleaning

It may be possible something was not reassembled or installed correctly and you may be running way lean of peak. After the first flight how did the spark plugs look like compared before the annual. It may be that some rubber part became twisted causing air leak during reassembly of one or second carb.  Check cross over tube, carburator boots and all hoses relating to carburetors for proper security and or cracks. 

After the first flight how did the spark plugs look like. You may even be running rich that could cause high EGT indicative of waisted. 

I may be totally wrong but I look forward to a solution soon regarding your problem. Hoping it will get resolved soon so myself can learn. Usually we look forward on a  better outcome following maintenance/preventative measures/inspections. 

Unlike other aircraft engines like lycoming where cylinder head temperature is a better indication of stress like say stay 340 or below F., rotax with water cooled head I may be wrong especially in cold weather maybe not be a good indicator of cylinder chamber stress. Hopefully if I am wrong I'll be corrected relating to above paragraph. 

I checked the spark plug and I found they looks stooy :-(  very black

didn't find any cracks on the hoses etc...

what it could be?

If spark plugs are black as stated, you are running very rich. Waisted gas not being used for power is entering exhaust manifold and pipe and burning causing high EGT. 

Something was not put together right after both carburetors were cleaned if all spark plugs black. Carburetors need disassembly and bing manual diagram needs to be used to make sure everything is put together right. Position of jet needle, long needle looking part, circlip  must be right as before. Make sure defuser, needle jet, mixing tube, and main jet, oring was inserted correct. O ring should not be twisted. Defuser so on and o ring can be checked without taking carburetor out if care is taken to make sure it was put in correct order,  direction and condition of O ring. Just snug when tightening back don't overtighten. Check to make sure it Is snug before unscrewing. Take ball of carburator and check to make sure parts have not fallen into ball because they were not tightened. 

Hope above helps and I am sure others will advise if any part I stated is wrong or ill advised. 

There is a good vedio in YouTube 24.48 minutes you might want to watch and could be one in this site to give you an idea what parts are called and assambly disassembly. If you do it, take pictures of every step of disassambly and plenty of notes. Bing manual diagram will also be crucial.

All was good before I assume before diassamby and cleaning. Parts replaced should have been correct. Very hard to see numbers on some parts without magnifying glass.

"If spark plugs are black as stated, you are running very rich".

We need to find out if his black plugs came from just idling or from high rpm run. Black sooty plugs are a norm after idling a while.

If EGT's went u significantly after carb work then I would suspect something wasn't done quite right. You may need to pull these off and have someone with Bing carb experience look inside.

After the second time the mechanic open, clean and replaced the nozzles and spark plugs we got WOT 5890RPM on the ground (before it was 5690 on flight)

So he set the prop to 5450 and now the EGT on 4340RPM is around 770 c but on climbing at 5100 it 820.  it seems like the high EGT come earlyer because the WOT is now 5450 instead of 5690. 

The plugs still looks sooty- black

The mechanic recomand me to change my carb filter but they are looks just fine, clean, with around 100 hours

e.g

I fly on PPC (AirWalf) so the The engine is completely exposed to air and use as pusher. I plan to re-set the WOT back to 5700/5750RPM (should I?)