The abs and low trac lights are likely related. ABS is the anti-lock brakes, and TCS is the traction control system which needs the anti-lock brake module to function correctly. The TCS lamp will come on with just about anything that sets a trouble code in not only the ABS but also many of the fuel injection system hard faults will cause it too. The TCS operates by the computer first quickly detuning the engine when it senses one of the front wheels spinning, which it detects through the ABS wheel speed sensors. Then if necessary the ABS actually starts pulse locking the brake on the wheel that is spinning, and that causes power to transfer to the other wheel, increasing grip, and reducing wheel spin. I suspect you have an ABS system issue that will need diagnosed.

The red arrow down lamp is a good question, I can't think of what that might be off hand. First suggestion is to check the owners manual and see what they are using that for, but of course somehow I expect your gonna say the car didn't come with the owners manual. I'm away from the shop so I can't even check my information system to see if its listed, but really I would not expect it to be, or at least it will be difficult to search for it by what the light looks like.