Can we create neutron star by pressing earth? Or other objects? Everywhere I can hear, that if we press anything to the right size, we create black hole.

Can we create neutron star by pressing, for example, our planet? And what if we press something bigger, like Jupiter?
It depends on what you mean by "can".

If you want to make the Earth into a black hole, you would have to compress it down to about the size of a marble.  That is impossible.  That is not just impossible with the technology of today, that is impossible with anything less than magic. 

However, if we did make an Earth-mass black hole, it would be stable. (Except to Hawking radiation)

Now if you could somehow compress the Earth into a slightly smaller space, you would need to overcome electron-degeneracy and at some point before making your black hole you would form neutron matter. This is impossible. Nothing can do this, not now and not ever.

An Earth-mass piece of neutron matter, however, would not be stable. Its own gravity is not sufficient to keep it from expanding, so it would very very rapidly explode. The same with Jupiter. A body needs to be larger than about 15% of the mass of the sun to have enough gravity as a neutron star to be stable. Jupiter has about 0.1% of the sun's mass

We can't create a small neutron star by compressing the Earth, unless we use magic, and if we stop squeezing it would explode.