The parity operator commutes with the Hydrogen atom Hamiltonian. The energy eigenfunctions are parity eigenstates with orbital parity $(-1)^\ell$ which follows from the fact that $Y_{\ell m}(\theta,\phi)$ is an eigenstate of parity with parity eigenvalue $(-1)^\ell$.
Question 1 What about the Helium (He) atom? The Hamiltonian of the He atom also commutes with parity but is not central. But I am not sure whether the energy eigenfuctions are still given by a product of a radial and an angular part with the angular part given by $Y_{\ell m}(\theta,\phi)$. So I cannot decide whether or not the He atom energy eigenstates also have the orbital parity $(-1)^\ell$?
Question 2 What about a meson $\bar{q}_1q_2$ i.e., a bound state of a quark and an antiquark? The strong interaction Hamiltonian commutes with parity. Mesons being strong interaction eigenstates (in absencce of weak interaction contamination) should also have definite parity. Can we say that mesons also carry an orbital parity $(-1)^\ell$? Apart from orbital parity there exists contribution from intrinsic parity which is not my concern here.