Quantum fields do indeed contain energy. In quantum field theory, particles are considered as excitations of their respective fields. These fields pervade all of spacetime, and their fluctuations and interactions give rise to particle creation and annihilation processes.
The energy of a quantum field is associated with the various modes of oscillation or quantized excitations within the field. Each mode can be thought of as a harmonic oscillator, and the energy of each oscillator contributes to the total energy of the field. These energy contributions are not fixed, but rather can fluctuate due to the inherent uncertainty of quantum mechanics.
Regarding your second question, it is not accurate to describe quantum fields solely as potential energy or potential energy fields. While there can be potential energy associated with certain interactions between particles or fields, the concept of potential energy alone does not capture the full nature of quantum fields.
Energy is indeed a fundamental aspect of the universe. According to the principle of conservation of energy, energy cannot be created or destroyed but can only be transformed from one form to another. This principle holds true in most physical processes. In the context of quantum fields, the energy associated with these fields is a fundamental component of the universe.
It is important to note that not all entities or phenomena in the universe are associated with energy in the traditional sense. For example, vacuum fluctuations or empty space can still possess energy due to the presence of quantum fields, even in the absence of observable particles. However, energy or energy-like quantities play a central role in our understanding of the physical world.