How do you replace the headlight bulb on a 2005 Dodge magnum ?

You need to replace the headlight switch most likely and the connector to to the headlight switch. Solder the new connector on and shrink tube the solder joints.

Obviously you have a connector which has come partially apart somewhere between the Headlights and the Headlight Switch. Most modern vehicles have several connectors between the Headlight Switch and the Headlights, Start at the Firewall Connector and work forward toward the Headlights making sure all connectors are securely mated. Another remote possibility is that you have fractured the "Low Beam Filaments" in BOTH Headlights. You don't mention how hard you hit the Speed Bump but if it caused the car to "Bottom Out" the front suspension it was a hard enough impact to fracture the filaments. You can use a 12 Volt Test Light at the Sockets for the Headlight Bulbs and see if you are getting 12 Volt power there. If you are in Low Beam position you have fractured the filaments. Check with High Beam too.

When its blinking fast look at both front and rear to verify which bulb isnt flashing. If the right works OK, then the flasher is OK. The flasher is INSIDE the front control module/integrated power module. If you cant find the problem, you may need a dealer to check it.

Disconnect the negative battery cable. Turn the nut on the cable clamp counterclockwise to loosen it and then slide the clamp off the negative terminal.

Step 2 Open the hood and remove the electrical connector from the back of the headlight housing ballast.

Step 3 Turn the headlight counterclockwise and pull the headlight out of the housing. You may have to angle the bulb up at a 45 degree angle to clear the frame and headlight housing

P0003 is fuel circuit volume low and P0061 is 02 sensor bank 2 sensor 3 heater circuit.

Generally a heater code usually means replace the 02 sensor. The heating element popped, kinda like a litght bulb does.

The 03 code will need further diagnosing to determine the exact cause.

He might not have done anything wrong.
If the headlight was ok before, then there's little worry that it won't light up after the guy replaces it.
Try cleaning the bulb holder with some elctrical cleaner. Check the ground terminal, fuse, swap bulbs.

The entire faceplate pops off. Then there are 4 screws retaining the climate control(sometimes there are just 2 staggered) remove the screws and on the backside you'll see the illumination lamp socket. Pull the socket out of it's holder and pull the bulb straight out.

you can get to bulbs, and screws to the tail light assembly, by pulling the liner by the light you want to work on

1, bad fuse. 2 both bulbs are bad. 3 bad groud wire. 4 check power to the bulb in trunk. bulb is not in the socket .