what effect does the presence of an extra neutron have on the chemical properties of new atoms formed
The addition of neutrons to the nucleus of an atom creates a new isotope of the element. It changes the nuclear properties of the atom, but has no effect on its chemical properties. Chemical reactions occur as the result of interactions between the electrons of atoms, not their nucleii so, for example, Carbon-12 and Carbon 14 will react chemically in exactly the same ways. The resulting compounds will have identical chemical properties but different molecular weights.
If you mean, new elements that are found, then you are looking at heavy and unstable elements. Such as elements 107 and above. So because you have 107 protons in the nucleus the neutrons add stability to the element by separating the positive charges.
Very little. As Rohan points out, chemical properties are almost entirely the result of the behaviour of electrons, so the mass of the nuclei matter very little. That's why, for example, all the halogens (F, Cl, Br, and I) have very similar chemical behaviour, even though their masses differ substantially (from 19. g/mol for F to 127. g/mol for I). The similarity in their electronic structure dominates the difference in their masses. Indeed, this fact underlies the entire structure of the Perodic Table, the fact that atoms of very different masses can nevertheless be grouped (vertically) together, in the Groups of the Table, because they have such similar chemical behaviour. However, there is a tiny effect, because the heavier atom has a lower zero-point energy of vibration in any chemical bond it forms. This lowers the bond dissociation energy very slightly. For example, the bond in H2 has a dissociation energy of 432.07 kJ/mol, while that in D2 has a dissociation energy of 439.57 kJ/mol -- about 7 kJ/mol higher. That will tend to lead to very slight differences in the rates of chemical reaction of H2 and D2. But you need sensitive experiments to even detect this.
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