"there is a proportional relationship between energy and mass" -> exactly. the mass of the system is strictly proportional to its total energy, and changes in t

"there is a proportional relationship between energy and mass" -> exactly. the mass of the system is strictly proportional to its total energy, and changes in the energy of a system will have a corresponding proportional effect on its mass. If you split the system into two components and release X energy, then the two components will weigh X/c^2 less than the whole system did; if splitting the system consumed X energy, then the separate components will weigh X/c^2 more than the original thing.