New rebuilt engine misfiring cel but runs great
 

So I bought a new rebuilt engine from Racingbeat, coils, leads and plugs and my mazda dealer installed them. However when the job was "done" there were cel blinking about second chamber misfiring when the engine was running 2k-3k rpm.
Mazda dealer said that it runs well. So they said that it might show the cel just because the engine gdoesn't have full compression yet. However after 400 miles it still occurs. Is this normal? I feel no power loss when the cel starts blinking.

If it's misfiring, it's not running great. Your dealer's response to this is bullshit. Misfires are nothing to screw around with on a rotary.

First, reset the ESS profile.
Turn ignition to "On" but don't crank the engine. Press the brake pedal 20 times in 8 seconds.

If that doesn't fix the problem, get yourself a bluetooth OBD-II adapter for $20 on Amazon and a phone app and start looking at short term fuel trim, long term fuel trim, MAF rate, coolant temperature, commanded AFR/lambda and actual AFR/lambda.

The dealer said that it was running fine because I saw no other sign of misfiring than blinking cel. I resetted the ESS already and no effect. The dealer said that the cel might be a mistake because of the compression. Maf was cleaned few months ago. Lambda #2 throws cel also but doesn't it just show if the cat is working. I ordered new lambda but I might have to get cat as well. Could bad cat affect in this. (It isn't red when I've driven a long trip)

That's akin to saying "you seem in good health, other than the constant vomiting". Ya need a new dealer, they're wasting your time.

Bad cat would normally make things worse the higher in rpm you go, but I wouldn't assume it's fine without inspecting it. You don't want to kill your brand new engine. You're right, the 2nd lambda sensor does show if the cat is working, so if it's throwing a code, what do you suppose that means? :) It would be helpful if you had the actual code, there are several. But, don't assume the cat is bad either and just replace it without diagnosing. That's an expensive way to find out it wasn't the problem.

As suggested above, start with the 20-time brake press to clear the ESS profile. That's a common thing to overlook when changing engines.

Either troubleshoot the problem or waste tons of money throwing parts at it. Your choice.

Ok I tried to reset ESS again and it worked. I guess that I didn't do it correctly for the first time (didn't check that oil gauge moved). Thank you!

Congrats and enjoy the crap out of your car!