What will happen if an electron and a proton collide? They attract each other inside an atom. But, why they don't collide inside atoms? Does the "boundary" of the nucleus push them away?

depends on the energy of the electron. For low energies, a bound state will be formed due to electromagnetic interaction between the two. In the case of higher energy, the proton can be transformed into a neutron. ~ Physics SE

How they can form a neutron? And, what they meant by bound state? While electrons have positive and protons have negative charge. They should collide and vanish, shouldn't they? (Another problem arises when thinking of thermodynamics: according to the first law of thermodynamics, energy can't be created nor destroyed. So, they have to form to another one if that so than, how they can form neutron? Is it responsible for charge?)