Transfer of infection from dentist tools? Is it possible?

Yes but not likely. If dental instruments are sterilized in an autoclave or chemiclave no bacteria, virus or fungus survives and you are safe. Almost all dental offices adhere to stringent sterilization techniques to prevent cross contamination from patient to patient.
Dental contagion. Without proper precautions and sterilization, a variety of infectiosn would be transmissible through dental tools, including: herpes, hiv, hepatitis b, and other more common viruses (colds, etc.).
Alway possible. But extremely unlikely. Dentists, physicians, and hospitals practice safe medicine by adhering to the "universal precautions" theory... That is, treat everyone as if they are diseased, whether they are or not. In this way instruments are sterilized and barriers are used to prevent cross contamination and spread of infection.