" As I understand it, electrons consist mostly of energy and the top quark mostly of mass" Not really. Both possess mass, and both are made of matter-energy, as are all things. 'Mostly made of mass' and 'mostly made of energy' don't make sense as concepts.
" Do protons, electrons and neutrons exist on their own or do they only exist in the nucleus of an atom?" Yes, easily. Electrons are free from atoms when they are conducting charge moving through a wire, and a 'proton accelerator' uses free protons.
"can a proton or neutron pass through the Higgs field and acquire mass, or is this the theory of how they DO acquire mass?" This is how everything acquires mass, but it's not 'passing through' the Higss field, we are all immersed in it all the time.
"Do they not have mass before they go through the HF?" Faulty question: the Higgs field is everywhere. It's a bit like asking if a fish was dry before it went in the sea for the first time.
" Are the protons that are found in the nucleus of an oxygen atom the same as the protons found in the nucleus of a carbon atom, for instance?" Yes, all protons are identical.
"Is it this "atomic mass" that is referred to when scientists speak of the mass of a particle?" Yes.
You could have looked all these up on wiki; as I understand it this page is for questions that don't really have firm answers.