The Alunar firmware you linked is a fork from the main Marlin firmware. If the bed Y direction is reversed, usually the stepper is incorrectly placed (mirrored) this is seen frequently for the Anet A8 printer which is very similar to your printer. In your case the X direction is wrong, this is usually related to the wiring of the stepper, reversing the connector by 180 degrees should do the trick (hardware solution). As a software solution, changing direction is not difficult in Marlin based firmware; you just want to invert the stepper direction; the following section in the configuration.h file does that for you:
// Invert the stepper direction. Change (or reverse the motor connector) if an axis goes the wrong way.
#define INVERT_X_DIR false
#define INVERT_Y_DIR false
#define INVERT_Z_DIR true
If your home position is still not working for you, you should look into this section of the same configuration file:
// Travel limits (mm) after homing, corresponding to endstop positions.
#define X_MIN_POS -33
#define Y_MIN_POS -10
#define Z_MIN_POS 0
#define X_MAX_POS X_BED_SIZE
#define Y_MAX_POS Y_BED_SIZE
#define Z_MAX_POS 240
MIN_POS positions as such that it starts at the corner of the bed. A more in depth bed center calibration tutorial can be found here.
P.S. Please do not print
anti-wobble caps for the Z-axis rods (as mentioned in another answer), these are not reducing the wobble, in fact they cause problems. What happens if you constrain the top is that you get a statically indeterminate construction; forces and displacements are not predictable! Better solutions to eliminate Z-wobble are lifting devices that decouple X/Y movement from the threaded rod (eccentricity of the threaded rod) from the Z movement. Also fixate the threaded rod above the springy stepper-to-threaded-rod coupler.