Right signal flashes quickly

you may have a bad flasher needing replacement. just because you hear it click when you turn on the signals does not mean the bi-metallic strip inside is working.

Fast clicking is caused by a higher than normal current being applied. Normally a short or a aftermarket relay that requires less current to switch. Sounds like the entire multifunction switch is bad.

That is a sign of a bad bulb, flashing fast. Check that rear bulb.

Check for power at the socket. If there is no power I would suspect the flasher relay wich supplies power to each bulb individually after it gets the right or left signal from the switch.

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I put aftermarket tail light and headlights LED in my in my truck 06 Dodge Ram 1500 turn signals got hyper flash trying to replace the relay cannot find

This is most likely going to be an issue with a relay. The relay on the fords that is tied into the blinker module can go bad is it gets wet or over loaded. Are there any after market things added to your vehichle? This can also be caused by overloading part of your ECU if you have after market headlights, or headlights that carry too high a load. When it blinks for 3-4 times and stops, does it blink faster than normal? This can be a sign of a false connection to the light itself. Such as having the wrong bulb in for the blinker.

I believe this car has a rear bulb that has two fillaments, one for side lights the other shared for braking and flash. sounds like a blown bulb or a bad ground connection. Check the bulb and the bulb holder and ground connection.
Turn signal blinking quickly generally indicates a blown bulb front or rear or bad connection.

your turn signal issue is very common even though you hazards do work they are on a different line connector in the relay that is also your turn signal relay. replace that hazard relay that should solve that problem. the c/v joints can be about 500 all the way up to almost 1000. depending on if you need the whole joint or just the boot kit. usually if you replace both joints they should swap your joints from right to left. which will make the clicking stop sometimes but if the damage is so bad that there are divots in the joint where the balls move you will need to replace both joints. and to be very honest going with after market c/v axles which allot of private shops do i have never seen one work without issues. not balanced right. as far as your transmission if you are low on transmission fluid due to an impact on your transmission pan that could cause that problem or if you have a shift solenoid going bad which can be very expensive. good luck hope that helped.

If your hazard lights work you need a turn signal switch, If hazards do not work replace the Flasher module

You will need to replace the flasher unit, I believe it is solid state, the old mechanical ones would just stop working, the new solid state one's do weird things like what you have going on.