Do Transformers store energy?

Transformers have a 'load' on their coil so they don't store energy as well as an inductor because the energy is transferred to the secondary coil. I think your last 3 paragraphs need some work. In most cases, transformers are not designed to store an appreciable amount of energy.

Can a battery storage system increase power system flexibility?

sive jurisdiction.—2. Utility-scale BESS system description— Figure 2.Main circuit of a BESSBattery storage systems are emerging as one of the potential solutions to increase power system flexibility in the presence of variable energy resources, suc

What happens if the current is removed from a transformer?

If the current is removed, they generate voltage or EMF. Transformers have a 'load' on their coil so they don't store energy as well as an inductor because the energy is transferred to the secondary coil. I think your last 3 paragraphs need some work.

What happens if a transformer is open circuit?

In a real transformer, if the secondary is open circuit there will still be some current flowing in the primary. That current is the "magnetizing current" and does result in some energy storage, but it is typically much less than the full load current.

Does a transformer transfer energy?

Since it is abstract, not physical, it doesn't transfer real energy. But in a real transformer, energy is transferred by way of the core. Energy is added on one side and removed on the other, more or less simultaneously. Inductors and capacitors do store energy. Are you OK with Faraday's law of induction?

Is a flyback transformer a switched inductor?

The flyback transformer is a misnomer and ought to be considered as a switched inductor with coupling, as it does store energy unlike an ideal transformer. However the addition of a small air gap allows more current with greater H fields now occupied in the air gap Not all the energy is in the gap but optimally it can be 2x as much as in the core.