Fuction of a Neutron

The neutron has a very important role in keeping the nucleus together. Neutrons contribute to the strong nuclear force (just like protons) that holds the nucleons (neutrons and protons) together against the electrostatic repulsion of the charge protons.

 

To emphasize this point, without neutrons, the universe would not have any atoms except hydrogen.

 

Very crudely speaking, yes. The force between nucleons is actually a residual effect of the strong interaction, and has about the same strength for protons and neutrons.