For example it was penertrated by a bullet via gun shooting, then it would recover itself in ten minutes. Is that possible for an organism to be this way?

No. Plenty of organisms can heal amazingly well, but nowhere near that fast.

Can such beings be created with scientific methods? Or is there a possibility to do that in remote future? I mean if the time for achieve it is infinite, will it be able to exist in our universe?

If you have infinite time and infinite resources, then you can do damned near anything you want. If only wishes and dreams were true... but, they're not.

It could probably be done, but at potentially serious cost. Allowing cells to replicate so rapidly and to differentiate so easily would make cancer much more likely.

However... what you might do is get some high tech skin graft, or spray on dermal matrix to essentially heal the wound in such a short time. Not exactly what is being asked in the OP, but accomplishes a similar goal in a much more realistic way.