We report on first experiments with a strongly interacting 2-D Fermi gas trapped in a single layer of a standing wave optical dipole trap. From in-situ imaging of the trapped cloud we obtain information about the equation of state of the system. A sudden release of the gas from the two-dimensional confinement results in an abrupt change of density, and therefore a quench to a noninteracting system. A very weak harmonic confinement in the radial direction caused by a magnetic field curvature leads to "matter wave focusing" after a quarter of the trap period. The momentum distribution of the gas obtained in this way reveals a bimodal distribution with a condensed fraction varying with temperature and interaction strength. We use this fraction to obtain the phase diagram of a two-dimensional Fermi gas in the BEC-BCS crossover.