You don't need the mathematics to understand. You do need something like it to standardize some concepts. You are stuck in a mathematical abstraction thinking and lose sight of physics. Look at your references to calculations and such.<quoted text>
No, you need the language to have the precision to talk about the ideas sensibly.
Velocity is also 'physical'. But it is calculated by dividing how far you move by how long it took. More accurately, velocity is the rate of change of position. And that is a mathematical relation. Acceleration is also 'physical', but it is calculated as the rate of change of velocity.
Energy is physical, but it is calculated by a variety of means, kinetic energy as 1/2*m*v^2 (in Newtonian physics), potential energy as the inverse gradient of the acting force, etc. If you don't have the mathematics, you can't see what is happening.
No, heat is generated when there is friction, which makes the molecules move more randomly. But a planet moving in orbit is also a 'load' acted upon by a 'force' that does not generate heat. And that planet has a kinetic and potential energy that add up to be conserved.
Friction is caused by molecules of two different objects trying to shear each other. Very, very small sawtoothy things pressed together by gravity or mechanical force, or even magnetically. The molecules aren't moving randomly, they are reacting according to the laws of physics which stresses their bonds and heat is generated. That is vibrations of the space surrounding them. You will also get heat generated by two charges displacing space around them. Your strong force and the motion is one example. Electric motors are another. Heat is transfered through the bondings of mass if present, the web of charges creating mass, or as light if not. This heat is your basic force, which is a vibration of the medium this universe was created in.