Is there a finite space for conservation of energy?

Your teacher's explanation is actually quite clear, but it uses a lot of physical language. In layman's terms, the conservation of energy is the conservation of time, as long as there is no work done on the object in a certain period of time, heating, etc., then energy is conserved at the beginning and end of this time. The reason why it is not said to be conserved in space is precisely because space corresponds to work.

Actually, you don't need to study it in such detail. Conservation of momentum is also a principle, the conservation of momentum requires that the object is not impulsed ft, therefore, there is a time limit. In high school, and even in college, there is very little quantitative thinking about space and time, so you don't need to do this at all.

It's a bit of a waste of energy

Space, like time, is a physical form that exists in the form of matter, and the propagation medium of electromagnetic waves is space, but electromagnetic waves are not the constituent units of space.

From a macroscopic point of view, the conservation of energy is the most basic physical law in the universe, no matter what kind of changes and matter, the conservation of energy is always true, so electromagnetic waves have energy conservation.

However, in recent years, some scholars have argued that there are conditions attached to the conservation of energy, but that is another level of discussion, and generally does not need to be considered in a normal understanding.

The bigger the space, the better.

Because momentum is vector and energy is scalar. Space is a vector, while time is a scalar. To show that two vectors are equal, directionality must be discussed, and to show that two scalars are equal, there is no discussion of directionality.

Your basic unit, the force itself is a vector quantity with spatial properties! Taking momentum as an example, when you talk about the accumulation of force in time, you have actually added the direction of the force, which is the accumulation of space in time. So this accumulation has a directionality, and its quantity must be expressed in a coordinate system in order to be unambiguous, and you can't explain its consistency in directionality when you discuss its accumulation in time.

For example, the momentum generated by two forces perpendicular to each other in the same time is perpendicular to each other and not equal. And when you discuss the accumulation of force in space, what you actually do is multiply the direction of force by the direction of space, so what you accumulate is an area that increases over time, and the area is also not directional, the expression area only needs to be large, and the change in the size of this area has time translation invariance.