If energy is drained from a capacitor linearly, does capacitor voltage decrease linearly as well?
If the energy inside the cap is decreasing linearly, how can the voltage be also decreasing linearly according to that equation?


In your circuit, the current source is absorbing or supplying energy, so the resistor is not the only place the capacitor energy can be transferred to.
When the capacitor is charged above 0.1 V, the current source will be absorbing energy, and when the capacitor charge is below 0.1 V, the current source will be supplying energy.

If you consider the energy absorbed by both the current source and the resistor, they will add up to the energy being discharged from the capacitor. 


  If you were to make an energy-time graph of the capacitor, you would see a straight linear decrease.


This is not correct.