Can particles be in positional eigenstate in reality? Do i understand quantum right in the following description? what we observed as particle is just the phenomenon they have some kind of quality corresponding to the macroscopic stones in experiments like photoelectric effect and the position of so called particles can never be observed precisely even after the collapse of wavefunction.
 A: Many eigenfunctions are idealised states that cannot occur in practice. For example when you learn about the hydrogen atom you learn that the orbitals $1s$, $2s$, $2p$, etc are the energy eigenstates i.e. the eigenstates of the Hamiltonian operator. However these states are time independent so they must have existed for an infinite time and continue to exist for an infinite time into the future. Obviously this can't be true (the universe hasn't existed for an infinite time) so these states cannot exist in practice. What we observe are very close approximations to them.
A similar argument applies to position eigenstates. These are Dirac delta distributions and have infinite uncertainty in momentum, along with other pathological features like infinite density. The best we would ever do is have a close approximation to a position eigenstate i.e. a particle localised to within some finite region of space.
Incidentally this answers your previous question Are the particles we see in a cloud chamber position eigenstates? since the tracks in a cloud chamber are, as you say in that question, just states localised to a small region of space and not position eigenstates.
A: The Heisenberg uncertainty principle , HUP, is a rule of thumb for observations of the very basic quantum mechanical structure of commutators. It helps understand conundrums that arise. In this case there exists a position operator, and the wavefunction of the particular system under study, in position space,  is the eigenfunction of the position operator , but that does not mean that this idealized mathematical situation can be used to represent particles measured in the laboratory. The HUP , if the (x,y,z,t) exact position eigenvalue were  considered as representing a real particle tells us that the particle should have infinite momentum uncertainty, and certainly it cannot be measured.
Real particles are represented by wave packets, a superposition of position eigenfunctions, and if you want to enter into the mathematics try searches, for example I found this lecture note, page 5.

This superposition solution is known as a wave packet
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