Firstly, I am not an expert in building robots, so someone may have a much better suggestion.

LED dimming
When you put a lot of power into the motor (AKA gunning it), you will draw lots of current.
When the robot is on the floor, the motors have to do more work than sitting on a bench (its got to drive around and move its own weight when it is on the floor) so they will draw more current.

When you draw current from the battery, the voltage of the battery will drop due to its internal resistance. So it makes sense that your LEDs will go slightly dimmer when you are driving around. However, a LiPo battery has a very low internal resistance so I would guess it should be fine?? (someone with more experience may know).

What batteries are you using? Are you pushing their capabilities?

Thinking about it more, there could be a high resistance in a connector or solder joint somewhere between the battery and where the LEDs break out (this would have the same effect as resistance in the battery).

Motors Twitching
I am not sure why the motors would be twitching. Maybe try adding a small deadzone on your controller and see if it helps? (sorry for not being much help)

Mysterious clicking noise
When you plug in the removable link it may create a small spark between the contacts. This may be what you are hearing. Is it one click? Or a series of clicks?

Footnote: The spark is caused by the capacitors in your ESC charging up and drawing lots of current. You can get anti-spark connectors to stop it sparking (there are some XT60 ones, not sure about other connectors). In my experience, as long as you can't see a lot of black/dark areas in the contacts where it has sparked, you should be fine (if you see anything, you can always post a picture).


I hope this helps, just let me know if you want me to explain something better.