My rear LHS indicator flashers fasters when I press the brake light also the brake light flashes as well.

Probably have a short in the electical system

It may be the elements of the RHS flasher bulb fused together..

it is probably a fuse. or a bulb gone, tends to throw everything else out and make it behave irratically when that happens.

Your rear RHS indicator has blown - replace it.

Hi you have an earthing fault on that side of the car. If the car is newish then maybe the ground wire has pulled out, if old then you have corrosion on the connectors.
This is a very common failure.

Youve got faulty wiring.

earth problem check where the wires got the body theres probably rust or if its a new bulb turn it round it may be in the wrong way

l bet its a ford, its quite common where car lights are in one cluster. wits down to a bad earth, so if you take the cluster out and clean all the connection with wd40 this should solve the problem

You've got a bad ground wire at the pigtail to the light recepticalplug.

You have a negitive short on your light cluster.

Bad earths or the wrong bulbs have been crammed into the light cluster.

Bad earth, or more lightly bulb has blown, check the bulbs

this has happened to me and it is when the bulb is about to go

Earthing fault, often cured temporarily with a smart clout! For a more permanent fix, take off the light fixture & clean all metal to metal contact, check wiring is intact.

check the bulbs are the correct bulbs, 1 pin and 2 pin and bulb connections are good, check wiring harness connections to lamp unit making sure connections are clean and tight, lastly identify the earth wire and try earthing the lamp unit. Sounds like you own a megane or clio.
Good Luck