Can i damage my canon t3i with time lapse photography?

I don't think it should be a problem, assuming you switch off live-view. 14 seconds should be enough time for the sensor to cool between exposures, especially at night when it is cold out, and 6 seconds per exposure isn't really all that long. Using live view would leave the sensor switched on all the time and that could cause overheat problems. If you are concerned then check your camera's manual and send an email to Canon. They should know what the camera's limits are.

No. The Camera is tested to 100,000 shutter count. The sensor will be fine. Its probably a good idea to turn of image preview, live view and info display to save battery and the screen.

Yes. You can definitely damage your camera with time-lapse. Your T3i is rated to 100k shutter actuations, which means you can take an average of 100k photos before the shutter breaks. In your terms, you can take about 200 sequences of 500 frames each. Of course, this is only an estimate and could vary greatly. Nighttime time-lapse won't damage the sensor, but prolonged sun exposure can. My suggestion, if you're worried, is to use a point and shoot camera for experimenting and your T3i for serious attempts. Good luck and hope this helps.