Answer
This is a question central to a nascent discipline self-labeled the philosophy of information, though clearly, it has roots in theoretical unification rooted in works like General System Theory by Ludwig von Bertalanffy. As such, what 'information' and 'energy' are is somewhat open to philosophical interpretation. Perhaps the most relevant philosophical terminology to your later edits are Das Ding-an-sich which posits that roughly offers that a physical state exists but is unknowable.
Broadly, information is anything which provides belief or knowledge, and energy is anything that causes work or changes in matter, both of which are context-dependent. In such a broad light, the questions are highly metaphysical, which is to say that they involve largely epistemological and ontological questions. We'll set aside the broader questions related to existence and knowledge and focus on the technically popular definitions.
For a lack of better terms, let's stereotype the popular technical definitions with Shannon's and Einstein's work. Shannon coined the term bit and began looking at all information as corresponding to a mathematical model (quantization entails measurement) and Einstein demonstrated the fundamental equivalence of matter and energy. To paraphrase Shannon, all knowledge can be stated or understood as a mathematical entity represented by binary numbers, and Einstein said that while mass and energy are neither created nor destroyed, they can be interconverted. The former is foundational to understanding digital information and communication technology, and the latter to understanding fusion and fission and nuclear technologies such as the atom bomb.
A good introduction into contemporary thinking about what exactly are information and energy is The Philosophy of Information by Luciano Floridi (though the prose is a bit florid, IMNSHO). It might be best to start with a notion of information that suggests that knowledge about the physical world that cannot be observed directly occupies a middle ground between the physical and the mental if one observes the basic dichotomy of naive realism. If one seeks to know, understand, and explain the physical, and one begins using technology to tackle open problems, one is inevitably left with the challenge of reconciling maps and territories and deciding what is knowable and what is not. A simple example is the Mach-Zhender interferometer that creates questions about information, energy, and action at a distance. This is where people start getting mired down between what is physical and what is mental.
Properly speaking, that is to say, on a literal reading under widely accepted precepts of analytical philosophy, information is an experience of an observer and is phenomenological whereas mass is held to be noumenological. Information is mental (rocks don't have information, but can be described by it), and mass inheres to the physical. If you have any knowledge of the history philosophy, the relationship between the physical and the mental is metaphysically contentious. Two very famous positions on this are Cartesian dualism and a rejection of it.