Temperature is defined as the average kinetic energy of molecules.

A) No, we cannot define temperature of vacuum.

Explanation

Vacuum is defined as space which contains no matter or space where pressure is so low that no interaction can takes place between any entities or matter. When there are no interactions, no molecule can form as formation of molecules requires Vander Waal force of attraction. So, temperature of a vacuum cannot be defined.

B) No, temperature of single molecules cannot be defined.

Explanation

Temperature for single molecule cannot be defined as we define temperature as the average kinetic energy of all molecules of a gas. And a gas cannot just comprise of single molecule. If that were the case, then there should be no need to do average. So, the answer is no.