The Homing error:
1. Check if all of the stepper motor wires are connected or fully plugged into the motors and the motherboard, sometimes they disconnect them for shipping.
2. Check if all of the limit switch wires are connected or fully plugged into the switches and the motherboard.
3. Check that all axises are free from obstruction within their range of travel.
4. Check if the tension on the belts that link the stepper motors to the axises have the correct tension.
The vibration is due to filament grinding.
1. The nosel is clogged. (Try heating up the hotend and manually moving the filament through, if not see 2, and 3, but if temp is correct, take apart hot end and clean it manually)
2. The heater cartiage is not heating the hot end to melting temperature. (Check the wires to and from the motherboard if connected)
3. The thermsistor is not working correctly, and therefore not allowing your heater cartiage to heat the hot end to melting temperature. (Check the wires to and from the motherboard if connected)
4. The temperature is set incorrectly, 170 to 210 for pla, etc...
5. Wrong sized filament, if the printer can only handle 1.75mm filament and you are using 3mm filament, this can happen.