Sounds like you have a short in your wiring harness for your rear lights. As for your dash turn signal light, your dummy light is just acting up. You probably need a new wiring harness for your rear lights.
Check the light control switch mounted on the steering column. The copper or brass switch block is not making contact.
It has been my experience that when the blinker comes on but the lights don't blink there is one or more bulbs burned out. If that is not the case check the flasher.
First of all let me say that most vehichles have 2 flashers, 1 for the hazzard lights and 1 for the blinkers. If you turn the blinker switch to either side and lights inside and out do not flash or light up then the most common problems are a blown fuse or the blinker switch itself could be bad. As for the hazzards blinking double time, it is possible the flasher could be going bad. One other possibility, autos that have had trailor light hookups installed have been found with bad grounds and/or wires that have rubbed into causing tail,blinker and stop lights not to work correctly
The tail lights are on a separate wiring than the blinker/brake lights. Look for a blown fuse or a broken/loose wire.
cheack the wireing
Probably Flasher
rear indcater lights very dim but ok when hazzards are on
whats the color circuit for the blinkers an break lights?
Check for a bad ground
The hazard lights get their power from the battery so if the battery is dead they will not work.
on blinker switch
Take the whole lens out