Yes... Any of the local anesthetics are usually in the 'caine' family. The most important part of the answer to your question is: was it administered correctly by the dentist, and was enough give. Dentist are very good at anesthetizing-:).
Yes. This is a good anesthetic and you should be fine.
Yes. Carbocaine does not have epinephrine, so its effects do not last as long as some other local anesthetics...For this reason it is not often used by itself to numb teeth for root canals. However, if your medical condition prevents you from receiving anesthetics with epinephrine, Carbocaine should be adequate, though it may have to be administered more frequently.