The scientific method tells us that the first step to creating or finding new scientific knowledge is to begin with an observation. Now the fact that this observation has embedded itself in the physical reality means that an application already exists. So suppose we observe that objects of different masses reached the Earth at the same time instant. We would then hypothesize an explanation for this theory which would then be tested experimentally. We find out that this occurs because Energy in a closed system is always conserved and hence we coin a new law called "Conservation of Energy." Now the very fact that Conservation of Energy is derived from a physical phenomenon means that it has an application (it explains why a feather and an elephant in a vacuum will reach the ground at the same time). Applying this kind of reasoning inclines me to believe that perhaps all scientific knowledge is applicable, although I would still like to read some counter examples (maybe some kind of theory that exists almost independently of anything else and has absolutely no application within or outside the domain of science).
Science aims at explaining our observations in the world. Hence the input comes from outside science. The explanation is given in the form of theories, often formalized by mathematics. The theory allows to make predicitions which can be confirmed or refuted by observation.
In this sense - input from observation and prediction of further observations - science is linked to the real world. But to predict observations does not necessarily mean to apply science. Application of the results of science is named technology. Here one has the aim to get some benefit from science.
An important confirmation of Maxwell's electrodynamics was the discovery of electromagnetic waves by Hertz. The technical application of this discovery is wireless communication.
Aside: That all masses fall with equal velocity in vacuum is due to the equality of gravitational and inert mass. I think conservation of energy is not relevant here.
I can think of two examples of questions which fall under the general category of science but yet would not be applicable to anything per your description:
- As it stands currently, string theory has no applications, since it cannot be tested, yet it is an active area of research, with symposiums, government funding, etc,...
- Speculation about other universes in multiverse cosmologies, and questions about what happened before the big bang, are frequently discussed by working scientists, and so would qualify as "science", but they have no application in the sense that you described.
That being said, most solutions to the demarcation problem (the problem of what constitutes science and what doesn't) tend to limit science to that which is applicable to the real world, almost by definition.