Yes, in literally thousands of experiments covering dozens of ways that particles can be entangled.

Entanglement can be verified a number of ways. The usually starting point is to generate a stream of particle pairs that exhibit a maximum of "perfect correlations". Only entangled pairs exhibit this, which is the cos^2(theta) function for photons. That reachs its max of 1 at theta=0 or 90 degrees. Unentangled photons follow a different correlation function, with a max of only .75 at those angles. The unentangled function is .25+.5(cos^2(theta)).

The next step is usually to form a Bell Inequality and demonstrate its violation. Obviously, for both the first step and the second step, the exact functions are dependent of the particle types, the setup, what is being measured, number of particles (entanglement can be 2 or more), etc. So the exact methodlogy varies, but is always described.

You don't prove a thing like entanglement (or gravity). What you do is to compare the predictions of different theories to see if you can dismiss some of those theories.

A large class of hidden variable theories make predictions that satisfy Bell inequalities. Quantum mechanics makes predictions that violate those inequalities. Experiments were performed, and the results weren't even close to satisfying the Bell inequalities. Therefore, those hidden variable theories have been falsified.

Note that violation of Bell inequality is only ONE aspect of the test of quantum entanglement. The other is the breaking of the diffraction limit using these entangled particles.

I'm sorry, I meant do the diffraction limit experiments (as Bell's experiments) favor the completeness of QM?. If so do the loopholes still apply to them?.
Thanks.

At some point, YOU have to do your own homework. We have arrive at that point where you have to read those experiments yourself, understand the physics, and then figure out if your question makes any more sense.

Look at the nature of the detector. In many cases, these are CCD detectors. It means that whatever is triggering it has a finite "boundary" of detection.

If I make the CCD camera pixels bigger, you get bigger "holes".

If you are asking about why the patterns are different, it looks to me that the electrons were diffracted through slits while the photons were diffracted through holes.

I know, I didn't mean that. If you compare the two patterns, you will notice that when photons go through the slits, they are more concentrated at one entrance point (tiny hole) along the slits axis unlike electrons.

No!, if you are sure about that, you would have said this before .

There are no loopholes in the proof of entanglement. What you are trying to refer to is the alleged loopholes in tests of Bell's inequality, which is used to rule out local realism. These are not the same things as proof of entanglement. Even folks that assert local realism is not ruled out by these tests must acknowledge that entangled pairs do NOT act like unentangled pairs.

I meant that you saw pictures of photons/electrons interference pattern before?.

Yeah, I know, maybe I should have said "entanglement interpretation". But have all the alleged loopholes been argued as not happening in Bell's experiment?.