When javier touches a hot mug of tea, energy is transferred from the surface of the mug to his hand. what kind of energy is this?

Thermal energy

Explanation:

Thermal energy refers to the energy due to the random motion of the particles inside a substance/objects. The faster the particles moves in an object, the more thermal energy it can transfer. This is also directly related to the concept of temperature of an object: the higher the temperature of an object, the faster its particles move, the more thermal energy the object can transfer.

According to the basic laws of thermodynamics, thermal energy (also called heat) is always transferred spontaneously from an object at higher temperature to an object at lower temperature. In this problem, the hot mug is warmer than Javier's hand, so thermal energy is transferred from the hot mug to Javier's hand.

see earlier

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.