Turn lights one side will blink but other will not

Sounds like an indication of a burnt out bulb. Check the front bulbs

yes it could cause the blinking red light.

both of the bulbs on the right side are busted

turn on park lights and signal on right side and take a good look at the front and rear light , see if one is dimmer than the other this may be due to a bad ground and when the park lights are on and drawing more power it also needs better ground, check the sockets front and rear try wiggling the bulb to see which one is causing the problem

Your right rear turn signal bulb is blown.Replace the bulb and the fast blinking will stop.

That is usually an indication of a blown bulb in the side that's blinking rapidly. Turn on the right side blinker and looking on the outside of the car, check all the bulbs that are supposed to blink and you will see on that is not blinking. Replace that bad bulb and the dash light will blink normally again.

This may have more then one bulb in the front or possibly a bad socket try wiggling the new bulb in the socket to see if it will work.Compare all turn signal lights that come on the passenger side to those drivers side.Some vehicles also incorporate sidemarker lights with the turn signals.

If the turn signals don't blink on both sides of the car, the culprit is the flasher, a small box usually located under the dash on the driver's side. Replace it with a new part.

If the turn signals don't blink on only one side, one of the bulbs on that side is burned out. Turn on the turn signal for that side and visually inspect the turn signals. Replace the burned-out bulb.

The blinking light is telling you that you have a headlight out, if you look the service light should be coming on when the light stops blinking.
Replace the head light and all should be fine.