Does alpha induced angle/"effective airflow" really exist in real life on 3D wing or this is just mathematical concept for calculate induced drag?

This induced angle really exist in real life on 3D wing. The physical reason why (what caused that induced angle) we see this induced angle is not the vorticity of the flow field though.

(same as lifting line theory-circulation theory is just math concept for calcualte lift ,but everyone knows that airflow dont move around wing in circle...)

I would not overgeneralize it as such myself. If you try to understand the derivation of lifting line theory I think you will be in a better position to appreciate it. Also, lift-circulation relationship comes from the Kutta-Joukowsky Theorem and not from the lifting line theory.

Also, the circulation is a generalized concept to indicate the strength of a point vortex. The general definition of the circulation is the integral of tangential velocity over any contour containing a point vortex. This DOES NOT mean airflow move around the wing in circles.

Question is ,if I put AoA-sensor in front of leading edge at same position at 2D and 3D wing,will be values different or equal?

Different values. In the 3D wing, the angle indicated should be lesser than that of the 2D wing.

(in my home made wind tunnel ,I cant see difference when I put visual AoA indicator in-front of leading edge at 2D compare to 3D wing..so this is reason why I ask is this real thing(maybe angle is too small to see) or just math concept...all this mess with questions about induced drag on this forum ,starts when I do this experiments..)

I for one would love to see some pictures of your home-made wind tunnel and experimental set-up.

PS1: This video from Doug McLean might be of help to understand it little better

PS2: As a completely general advise, Unfortunately, Its a little difficult subject to follow "Correctly", and as in any other scientific discipline, the problems and solutions tend to lie in different places than the majority of the people think where they are; so at least in a long run, probably it's a good idea to learn at least the basics enough to validate what's thrown your way. There are few very good free online courses on edx.org