Question

Can we change an element to another element by changing the number of protons and electrons in it?

Answer 1

By changing the number of protons of an element, you are changing the element to another element.
By adding a proton to Neon (22) you changing it to Sodium (23)
Adding a proton may cause the element to be unstable.
By changing the number of electrons you are creating an ion. This makes the atom either lower in energy or higher in energy.
If you could magically make two neutrons in the nucleus of an atom disappear, the atomic number and the electrical charge of that atom would remain unchanged. Neutrons do not carry an electrical charge so adding or removing them from the nucleus does not change the electrical charge of the nucleus. It does, however, change the mass of the nucleus. Adding or removing neutrons from the nucleus is how isotopes are created.
Protons carry a positive electrical charge and they alone determine the charge of the nucleus. Adding or removing protons from the nucleus changes the charge of the nucleus and changes that atom's atomic number. So, adding or removing protons from the nucleus changes what element that atom is! For example, adding a proton to the nucleus of an atom of hydrogen creates an atom of helium. (Actually, a few neutrons have to be added as well to make the new nucleus stable, but the end result is still helium.) Keep in mind that atoms, by definition, are electrically neutral and always contain the same number of protons and electrons.