Are your teeth technically alive? This isn't such a straightforward question. Your teeth are actually made of different layers, and some are more alive than others. The hard, outermost layer of the tooth is its enamel. This is the strongest substance in your body; but when it's gone, it's gone. Damaged or decayed enamel cannot regenerate. Beneath the enamel is dentin, and this can regenerate itself to a (very) limited extent.
Which tooth is the hardest worker in your mouth? They all have their part to play, but in terms of physical effort, your molars have a lot to deal with. Your upper molars press down into your lower molars, masticating, grinding, and generally pulverizing food, processing it into a manageable consistency to be swallowed. Adults should develop 12 molars (three on each side of the upper and lower jaw), including wisdom teeth.