What does umbilīcus mundī mean in Latin?

umbilīcus mundī, a noun, means “the 'navel of the world', an omphalos considered to be the axis mundi”.

What is the genitive of umbilīcus mundī?

The genitive singular is umbilīcī mundī. umbilīcus mundī is second declension.

nounsecond declension

umbilīcus mundī m (genitive umbilīcī mundī)

the 'navel of the world', an omphalos considered to be the axis mundi
Equidem terra ubique gentium ad umbilicum mundi fertur in hoc mundo,1565, Lucilli Philalthaei, Philosophiae, Medicinaeq. Professoris Publici, ...:
Est & vox haec translatitia ad medium cujusvis rei signandum, ut quum vocant Delphos Umbilicum mundi, videor & in Verrinis legere, [...]1727, Pieter Burman, Sylloges epistolarum: a viris illustribus scriptarum tomi quinque: