Right rear blinker problem

There should two separate bulbs for marker and blinker. It sounds like a bulb is burnt out, bad ground, melted socket or a wiring anomaly. Are you certain it's supposed to have 57 series dual element bulbs for blinker and markers?

What about the front right turn signal, does it work when the rear doesn't? My guess is, it doesn't work either? The lower brake lites and turn signals may use the same bulb filament, but, not at the same time and are wired through the turn signal switch. Have you tried a new bulb, Is the bulb socket ok? You may need to check turn signal switch and wiring. If there is an air-bag in your steering wheel, you need to be careful, you don't want it to blow up in your face. Safety is your responsibility.

The signal wire going to the right front has a splice for the dash indicator, a wire branching off from the turn wire and going to the dash. It sounds like that right signal wire is broken or lost a connection before it splices off to the dash, so the problem sounds like it is under the dash, either coming out of the turn signal switch to the flasher or from the flasher to that splice. You may need a multi-meter to check voltages on that wire at various places under the dash. Ascertain which color wire you need to concentrate on. Check for voltage on it with key on and right blinker on-voltmeter will spike to battery voltage, then fall to zero as the flasher breaks voltage continuously, if checked after the flasher. If checked when leaving the turn switch, it should be a continuous signal on that wire. Think you better find a wiring diagram to find the right wire to check. Good luck.

sounds like the relay is hosed. Turn on right blinker and follow the blinker sound under the dash, usually. Usually the other relay will be right next to it. The relay turns the voltage on and off to make it blink

Yes - the fast flashing is a warning that a bulb is burned out. Change the bulb (be careful to put it in the same as the old one as it probably is 2 bulbs in one , parking and turn/stop) and you should be fine.

The fuse for the turn signals is located in the interior fuse panel, usually located under the dash on the drivers side although it may be behind a panel on the side of the dash on the drivers side that you can access when the door is open. The flasher relay is located on or near that fuse panel as well. There is only 1 fuse for the turn signals so if you have some of them but not all of them it's not the fuse. It may still be the relay but I doubt it. That bulb may not look burned but it most likely is. that fast blinking on the right rear is an indicator that the front bulb is burned or not functioning. It is an indicator dodge built into there lighting systems. Replace the bulb, if that doesn't resolve the problem start check the wiring and look for a grounded wire.

The right blinker issue sounds like you have one bulb out either front or rear check them both. The left blinker issue sounds like either bulbs(both out) or fuse, or worst case blinker switch has gone bad on left turn only so not picking up the signal.

make sure our lights at rear are grounded sounds like a bad earth

the fuse is broke

Pull that bulb out and look closely at it, it'll probably have one of the filaments(Tungsten wires) broken and crossed over to the other one causing a short to power and/or the bottom of the bulb has had the 2 lead contacts melt together. In either case the bulb will need to be replaced. If this doesn't fix the problem please let me know so I can look into it further.