The helium atoms must be bosons. The atom includes the two spin 1/2 protons, the one (He-3) or two (He-4) spin 1/2 neutrons, and the two spin 1/2 electrons. Angular momentum is a vector, so the possible spin angular momenta for the atom are the possible vector sums of the particle momenta. If the result is integer, the particle is a boson, if half-integer, a fermion. The easiest way to see the result for any given composite particle is to figure the maximum value of the spin, which is just the number of particles times 1/2.
Hence: He-3 has 5 particles, so max spin is 5/2, it is a fermion. He-4 has 6 particles, max spin is 6/2 = 3, it is a boson. An H atom has two (proton + electron), so max spinis 2/2 = 1, a boson.
The protons and neutrons in a nucleus do not overlap, because of the Pauli principle. Thus the nucleus has a finite size, roughly the size of all the nucleons gathered into a liquid lump. For the same reason neutron stars have a finite size.
There appears to be confusion about the nature of the condensate: it is not that the atoms are all in the same place at the sametime. This could not except under very weird conditions be an eigenstate of the Hamiltonian. Rather it is roughly that theparticles all have the same momentum (and it is zero) at the same time.