I cannot move the passenger side headlight out to change the bulb

Raise the hood and find the 4 push-in retainers that go along the top of the front grille. Then when you pop off that trim on the headlight you will have a little room to work with. Remove those retainers. Get a flat-bladed screwdriver and a rag, place the rag above or below the trim on the headlight. The rag will protect the headlight from getting scratched when you pry up on the trim with the screwdriver. The trim will pop out towards you. That should give you enough room to remove the headlight. There are two hex-headed screws right on top you can easily see holding the headlight and then one more if you lean in and look down further. Remove the 3 bolts. Now just wiggle and lift up on the headlight and it should come loose. You may need to unplug the side marker bulb wiring to give you more room. Keep the rag wrapped around the trim piece to again avoid scratching the headlamp. Then you will see the big round black plug cover to turn and remove to gain access to the bulb. The bulbs are halogen type bulbs so don't touch them with your hands. The oils from your skin will cause the bulbs to burn out prematurely. Use a clean cloth to handle the bulbs. Reinstall the headlamp the same way you removed it. You will see how it goes back in once you get it out.

you might need to move the air filter box to do this.

The bulb and its wiring is on the back of the headlight. Twist the clip to remove it from the headlamp housing, pull the bulb out and replace it, then reinstall the bulb into the housing.

If you need to replace the whole headlight and not just bulb you'll need to remove the grille by unscrewing 4 screws on the top side of the grill Rotate the grill toward the front to release from the clips holding it in place. There are 2 screws on the inboard area of the headlamp. Remove these two screws and the lamp will come out. Now you can replace the lamps or the unit.

Drivers side- stick your hand behind the headlight and remove the rubber cover, and twist out the light.

Passenger side- remove the air cleaner top, and move the air cleaner out of the way. You now have complete access to this side to remove the rubber boot covering the bulb.

There are two retaining tabs on the back side of the headlight. One on each side. You must pull up an the tabs, then the whole assembly will come out. Then twist the bulb socket out.

Drivers side- stick your hand behind the headlight and remove the rubber cover, and twist out the light.

Passenger side- remove the air cleaner top, and move the air cleaner out of the way. You now have complete access to this side to remove the rubber boot covering the bulb.

Drivers side- reach hand behind headlight and remove the rubber cover, then turn and remove bulb.

Passenger side- remove air cleaner top and move the air cleaner out of the way. Now you have access to the rubber cover to replace the bulb

to change passenger side headlight bulb,on 04 plate yaris, remove bulb cover at rear of lamp,take off fuse box,although this only gives you slightly more room,and have someone with small hands,replace bulb,as it is nearly impossible if you have large hands.It is awkward but can be done,EVENTUALLY.

The procedure doesn't call for removing the headlight assembly. It is as follows:
The high beam headlight bulb and the low beam headlight bulb are replaced the same way.

Open the hood. To change the high beam headlight bulb on the passenger’s side, remove the power steering fluid reservoir from its holder by pulling it straight up.

Remove the electrical connector from the bulb by pushing on the tab and pulling the connector down.

Remove the bulb by turning it one quarter turn counterclockwise.

Insert the new bulb into the hole and turn it one-quarter turn clockwise to lock it in place.

Push the electrical connector back onto the bulb. Make sure it is on all the way.

Turn on the headlights to test the new bulb.

If you replaced the high beam headlight bulb on the passenger’s side, reinstall the power steering fluid reservoir.

Hope this helps, but if you are having some specific problem leave a more detailed comment and I will try to help you.

TEST
remove both bulbs from the lamps but leave them on their wires switch on and see if the bulbs are still different brightness if not they the passenger side lamp housing has damaged mirror is dirty or missalined and needs adjustment. if they are different brightness then this may be a earthing problem.

Well, forgive the generic response.. I have done loads of Honda... but not a 2003 Civic...So, here we go..

Open hood. Locate top headline tab. Remove screw that secures tab.
Next, locate nut on backside of headlight assembly - remove it (it should be a round fastener that has a hex nut top.
Headlight should pull away from chassis.
Connecting cable has a lock tab that must be pressed. If you just pull out on the cable assembly - a large, round (2.5 to 3 inches in diameter) water proofing shroud will come out of the headlight assembly - bulb and all. You will still need to remove the cable connector from this assembly.

Install a new headlight assembly in the reverse manner.