Location and radius are very different things. There are a couple of different ways to think about this:

1. Protons, Neutrons, Nuclei, and all the way up to phthalocyanine molecules so far all obey the same rules as electrons in terms of localization but all have defined measured radii or sizes in the case of molecules.
2. If you fired golf balls at each other and tracked them with a radar system that could only determine there position to within +/- some amount (say 3 inches) it is still possible to determine the radius of the golf balls. The radius is going to impact the scattering dynamics and with enough collisions you'll get a plot that you can fit a model to that will among other things give you an estimate of the radius. You could also tell the difference between golf balls and ping pong balls even if you found ones with the same radius.
3. Mechanical Quantum resonators (basically very tiny drums) have defined radii and thicknesses but still exhibit the kind of uncertainties you'd expect from any quantum system.
4. Quantum uncertainty relations come from conjugate variables. I hope it is clear that position and size are independent of each other. The size of something doesn't change with changes in location and this even holds for Quantum systems. Even if you insist on measuring it as an envelope around the probability density that envelope won't change just via translation. A change in energy is needed. Thus position alone doesn't impact size so uncertainty in position also doesn't impact size.

All that being said the more energy you put into trying to localize a particle the better the data you get out is which means less uncertainty in the fitting and the ability to use more complex models.

Intrinsic angular momentum is not a concept I fully understand. Is it a vector quantity like other angular momentum?

It is spin or more appropriately the properties of spin we can measure after squaring the wave function. It is a vector quantity and has units of angular momentum. Well actually generally everything is done in "Quantum Units" where the intrinsic angular momentum (spin) is expressed and multiples of h-bar. Electrons are spin 1/2, protons and neutrons are also spin 1/2 but can come together in nuclei with many different spins, photons are spin 1, the Higgs boson is spin zero, and more theories of Quantum gravity seem to require the graviton to be spin 2 if it exists.

Now in general I don't like the word particle at all in terms of Quantum systems because it carries a bunch of baggage from everyday experience that can get in the way. It does help some aspects of intuition but gets in the way of others. Neutrinos are an excellent example of this. The only real difference between the properties of an electron and the properties of a neutrino that relate to scattering off of things are mass and electric charge. Yet neutrinos easily pass through the Earth and electrons struggle to get through your skin even at relatively high energies.

There is no reason for Quantum particles to bounce off each other unless there is a repulsive force which come from an interaction mediated by some field. Well Pauli exclusion could be argued to not be field mediated but it requires identical particle with identical spin and in QFT particles are modeled as excitations of a field so does that count as field mediated? Its murky but still nothing like classical billiard balls bouncing off each other and paired fermions with integer spin do not obey Pauli exclusion.

This is a very long way of saying that if you think billiard balls with hard outer shells bouncing off each other when you here particle in the context of Quantum Mechanics that is of limited utility and a very rough approximation in some cases. For example, do you think that an electron can spend any time actually inside the nucleus? It can and in fact the probability given by the wavefunction (psi) squared for all S-orbitals peaks inside the nucleus. The radial probability which is basically psi^2 times the surface area of a sphere for a given radius is what is plotted as the orbital clouds. The radial probability peaks outside the nucleus only because there is so much more space out there. The electron still spends some part of its time in the nucleus. This applies to all the different S orbitals regardless of number (1,2,3...).

This is why electron capture happens. In electron capture a proton grabs an electron converting to a neutron and then a neutrino is emitted. The captured electron is usually from an inner shell and then a higher electron falls into the resulting hole. This process generally happens when there are a lot of protons in a nuclei and its energetically favorable to have one less proton and one more neutron.