You don't have to give them any medicine unless they are sick, with the exception of a good dewormer every 6 months as a precaution, if your chickens are kept on the ground. You can have them vaccinated against a number of diseases, such as Newcastle, Mareks, etc. There is more information on the different vaccines here: http://edis.ifas.ufl.edu/ps030
No, not unless it grows excessively long. They need their beaks and claws to do chicken things, like scratch and peck, so don't trim or cut it unless you need to.