Does the auto thrust at takeoff compensate for asymmetric engine characteristics? When a percentage thrust has been determined for take off the auto thrust system (Airbus) or the auto throttle (Boeing) will send the data to the engines FADECs to provide the required thrust.

When the levers are set at FLEX (Airbus) or when the levers push button is pressed (Boeing) the engines will develop the takeoff thrust which is displayed as an N1 or as an EPR.

It seems the FADECs will command the same N1 (EPR) for all engines since the displayed N1 (EPR) are the same for both (all) engines. Am I right?

Considering the engines may have different age and therefore producing different thrusts for the same indicated N1 (EPR), a thrust assymetry will result. Is it true? How this is acceptable at take off?

Considering the engines total running hours (aging of the engine) are known by the operator, is there a way  to enter such a data to the auto thrust or to the auto throttle or to the FMS in order to get at take off really equal thrusts and not just equal N1(EPR)?
@JuanJimenez's comments are correct. N1 (and the accuracy of EPR) are not indicators of a precise thrust force.

So to answer the title question, generally no, moreover the acceleration of each engine may be different, and that is why the pilots go through a stabilization step, where they apply some thrust, make sure they're responding in a sufficiently similar manner, then they proceed with takeoff thrust. The pilots will correct any yaw with the rudder, and any remaining effect could be similar to a very light crosswind.

Also see: How is thrust of engines on the two sides of an airplane kept exactly equal to prevent yawing? The same phenomenon due to wear and tear is discussed. It is trivial for the most part since there is a rudder.

Of course this affects fuel consumption in-flight as there will be a tiny yaw as well that needs to be trimmed out.

But don't take it from me, check the Airbus article, Engine Thrust Management - Thrust Setting at Takeoff.


  Every engine has its own performance level due to manufacturing tolerances. In addition, engine performance evolves with time due to wear and ageing. As a consequence, the acceleration profiles may slightly differ from one engine to another on an aircraft (fig.3), even if fitted with new engines.
  
  Similarly, the idle thrust can slightly differ from one engine to the other, moving the acceleration profile to the left on the graph (fig.4).


Earlier I said generally no, because there are always exceptions (never say never on the internet). The articles notes that the Trent engines of the A330 and A380 automatically manage the stabilization step.




RE notice: On old aircraft before FADEC pilots were manually adjusting the thrusts to be equal (...)


It's because before FADEC the link between each lever and engine was a cable, and each cable depending on its age and environmental factors, acted differently – different stretching, friction, set torque, etc.

With FADEC, this is no longer a problem. The same electronic command is sent. And depending on the target, e.g., x N1, this is what the engines aim for, regardless of each engine's age and the fact that exact N1 values don't mean the same thrust force. Pilots pre-FADEC, like pilots with FADEC, don't know the thrust that is being applied in lbf/kN.