No, you'd better not wear it and buy new one instead. That because the torn contact lenses will hurt your eyes seriously. It is likely scratch the lens of your eye and even harbor some bacteria. So, you'd better take them out immediately for the sake of the health of your eyes. And next time that happens, try to put your eyes some eye drops or saline solution to moist your eyes and then get the lenses out of your eyes.
You should stop wearing them! The torn parts are much sharper and rougher than the normal edge and can scratch your eyes. Your vision will be slightly off if it is more serious. You will also not feel comfortable with it. I would suggest getting new ones or seeing if you can get the torn one replaced most places will do it for free if you say that it was torn via shipping!
Of course not. If your contact lenses are torn, no matter how slightly they were torn, I strongly suggest you to stop wearing them immediately. Because the torn contact lenses would hurt your eyes' cornea and thus cause a lot of eye diseases, which would be really bad for your eye health.