What would happen if an electron collided with a proton such that the two do not collapse? Would the two become a unit, or would some force prevent them from bonding thus forcing the electron to orbit around the proton?
I'm not sure what you mean by "collapse", but if I interpret that as "no hydrogen is formed" or "the electron is not captured", then 2 things can happen:
1) Elastic electron-proton scattering: the electron and proton just "bounce" off each other under some angle theta. By observing the cross section of the scattering versus the theta angle it was shown that proton is not a point particle, but an extended object.
2) Deep inelastic scattering: the incoming high energy electron "destroys" the proton into a bunch of outgoing hadrons (mostly pions). By observing the cross section of this interaction it can be shown that proton is composed of pointlike particles. The electrons collide elastically with a parton.
Some details are here.
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.