Anti-neutrons, anti-quarks, isospin: What is observed and what is derived? I would be a little more restrained with the existence of antineutrons. First at all - if I understood right - the existence of antiquarks is hypothetical. If one not agree with this please refer to experimental data which shows their observation.
Second one has to show that the neutron is not able to decay in electron, neutron and anti-neutrino as well as in the anti-particles. If one will use the isospin he has to go back in history and to explain how and why the isospin was discovered. Or was he invented?
Third a neutron-antineutron collision - after all what we have seen in this kind of collisions with protons-antiprotons and electrons-positrons- has to lead to pure energy in the form of photons. Did we get this data in some experiment?
 A: You didn't understand any of these questions right. Antiquarks and their bound states, including the antineutrons, are produced and observed as easily as bread and butter. Lots of details experiments with e.g. antineutrons have been performed, e.g. 

Scattering of antineutrons with hydrogen
http://www.sciencedirect.com/science/article/pii/037026939290998J

(this one was done more than 20 years ago) and all these experiments agree with the theoretical predictions. Millions of antiquarks are produced at the LHC each second (when it's running), too.
There's not a tiny doubt that every particle has an antiparticle. For most particles, the antiparticle is different from the original particle. Only "truly neutral" particles such as photons, gravitons, and Higgs bosons (but not neutrons!) have antiparticles that are identical to the original particle. All the antiparticle species to the known particle species have been observed, too.
The neutron always or virtually always decays to a proton, an electron, and an electron antineutrino. There's no doubt about it – this fact can be calculated from the Standard Model and it may experimentally verified, too. 
Also, the antineutron can't decay to the same products as the neutron (or vice versa). That would violate the conservation of the baryon number and the conservation of the isospin in the processes based governed by the strong interaction. These conservation laws are "laws in our theories" but we only believe all these laws because there is an overwhelming experimental support for all these things.
It's impractical to measure the neutron-antineutron annihilation because both particles are (equally) unstable. But totally analogous annihilation of antineutrons and protons (see the paper above) – with some light charged products aside from neutral pions – are almost the same thing and indeed, virtually all the rest mass gets converted to pure energy just like in the case of any annihilation.
All the things you doubt – and hundreds of much more advanced, detailed, and accurate insights of a similar kind – are completely indisputable and experimentally verifiable, often very directly.
A: 
First at all - if I understood right - the existence of antiquarks is hypothetical. If one not agree with this please refer to experimental data which shows their observation.

Everything we observe can be considered hypothetical for each of us. It is a hypothesis that you have a screen and are reading this. Maybe it is all a hypotheis  in my mind , or your mind. Everything coming in from our senses is the real experimental data.
Fortunately we have managed to have a common data base and to start with defining experiment and the data. In classical physic this means measurements in thermometers, balances etc defined a set of data that could be modeled with classical thermodynamics, classical mechanics and classical electromagnetism. It is with mathematical formulae that we predict the orbits of satellites, and the model is validated because new measurements show that the satellite appears where we calculated. Nevertheless it should be clear that the numbers we measure and are fitted by the mathematical model are a type of "proxy" of what one might call "real" behind the numbers.

Second one has to show that the neutron is not able to decay in electron, neutron and anti-neutrino as well as in the anti-particles.

This decay makes no sense.

If one will use the isospin he has to go back in history and to explain how and why the isospin was discovered. Or was he invented?

Then we come to the quantum mechanical framework and special relativity, both extremely crucial in understanding and modeling nuclear physics processes.  The models are extremely successful ( viz atomic bomb and nuclear reactors). Isotopic spin has been defined within nuclear physics where it was discovered that for many states whether a neutron or a proton was involved a symmetry could make predictions. The SU(2) symmetry of isospin organized nuclear reactions in a coherent model. Actually several models for calculation purposes but isospin is necessary for all. The concept of a baryon  arose from this symmetry, since for the strong interaction , of which  the nuclear force is an expression, protons and neutrons are interchangeble. Note that we are down one level in the proxies necessary to call a measurement a measurement, i.e. a validation of a model. More complicated detectors than thermometers and balances are necessary. 
The data and the models fit so well that it is ridiculous to question whether isospin works or not or was invented.
Then we come to particle physics which has been studied extensively and is modeled correctly with the standard model, which is to all intents and purposes a shorthand description of innumerable measurements in particle physics.

Third a neutron-antineutron collision - after all what we have seen in this kind of collisions with protons-antiprotons 

Proton antiprotons annihilate into pions mainly and this has been documented/measured so well that it only displays ignorance to question it. 

please note the the pi letters are put in after the photograph of the reaction was taken 

and electrons-positrons- has to lead to pure energy in the form of photons. 

Even more wrong in the case of energetic electrons and positrons as in LEP


Did we get this data in some experiment?

yes we got these data from a lot of experiments and keep getting it and planning new experiments.
repeat of first question:

First at all - if I understood right - the existence of antiquarks is hypothetical. If one not agree with this please refer to experimental data which shows their observation.

Quarks antiquarks and gluons come from the level of measurements that is even more removed from thermometers and balances, complicated detectors that need thousands of physicists and engineers to construct and maintain and take data with. And they come because the hypothesis that they exist allows us to have a definitive model of how particle interactions work. We have particles as traces in the chambers, we have seen quarks and gluons as jets in the particles produced in the elementary interactions ( one more level in measurements). We say we have "seen quarks and antiquarks and gluons" because the model, SM,  we use to interpret our measurements demands that they are there. The model fits the data up to now very well and has made successful prediction for new observations, the most recent one the discovery of the Higgs boson.
A: 
First at all - if I understood right - the existence of antiquarks is hypothetical.

Your understanding is entirely incorrect. Anti-quarks are a work-a-day reality in the particle physics world.


*

*The annihilation of quarks and anti-quarks to form lepton pairs (i.e. Drell-Yan scattering) is not merely regularly observed, it is used a physics tool to probe the anti-quark content of the nucleon sea in experiments such as NuSea and and SeaQuest.

*The reverse process (electron-positron) annihilation to lepton free hardron states by way of a quark/anti-quark pair allows one to measure the charges of the heavy quarks directly. 

*The lifetimes of neutral pions are consistent with their proposed valence content (a mixture of quark/anti-quark flavors) while mesons with valence content that is not a quark/anti-quark pair must find slower decay routes (i.e. weak decay for charged pions).
