How could you predict degenerate pi molecular orbitals just knowing what symmetry point group a molecule belongs to?
Which orbital symmetries you can get in a molecule always depends on the molecule’s point group. Only for those point groups which have degenerate irreducible representations can you get degenerate orbitals; so out of your examples only the $D_{4h}$ molecule could. This is entirely independent of Hückel’s method to determine energy levels.

But just because your molecule has the irreducible representations, doesn’t mean that a $\pi$ orbital has to have that degeneracy. Instead, it again depends on what you get when following symmetry rules.

You can calculate whether you will get $\pi$ degeneracies by drawing your molecule of interest, including all the p atomic orbitals and determining the molecule’s point group. Once you have that, for each symmetry operation, check how many p orbitals would be transformed onto themselves by said operation (and note whether with or without a phase change). Add that up. Once you’ve done that, you basically have the representation of the p-orbitals of the molecule that you can reduce to irreducible representations, finding out how many discrete and degenerate energy levels you have (albeit not including energy values).