In the case of the energies it is hard to have a decent discussion.
The eight energies are actually two sets of four reciprocal energies, which are themselves made of two aspects, substantial and insubstantial.
The ideas of fire and water have very little to do with the teaching in most formal schools, it is better to see it in terms of the substantial inside the insubstantial and the reciprocal of the reverse, the insubstantial inside the substantial. The trigrams show this well, but the interpretations of the trigrams do not, ergo fire and water are essentially irrelevant, which is why the formal teaching uses the names of the trigrams but does not employ the concepts of fire and water. In the formal teaching fire is mentioned for one of the five directions, or movement aspect that form an essential aspect of the 13 postures, however this is given in the five element form to teach a functional and dynamic relationship, the directions do not have inherent properties of metal, wood, fire etc, which is why it is said that it is all the same up or down, front or back etc.
It is not that forward is metal, it is that in relationship to another direction forward is a dynamic answer, the essential functions of this scheme describe vectors of force for neutralization, again shared to be the same on any plane, be it vertical, horizontal or diagonal. The force vectors are at perpendicular angles and this relates to the formal teaching that force is never met directly, in this way the five element scheme is illustrative not of elemental properties but of how force is neutralized.
An is an energy, not an application, when it is said to be push it is not meant as an application as anyone taught formal applications already knows. In terms of the Bagua trigrams, and the resultant combinations which correspond to the i-Ching, what is described and taught is essentially physics, not application in the formal sense, the energy of an can be put into many motions, as is the case with all energies, there are different teachings directly relating to application. In this an is indeed an attack, and Gord is right that it is not a formal push, however the energy can be described as pushing, much like Ji can be thought of as a press, such as a lever squeezing down on a plane from a fulcrum or axis, for this reason both press and squeeze are correct in terms of the realization of the energy, and both are incorrect as formal applications.
In terms of applying trigrams in combination as hexagrams one can understand the teaching as sequence, employing two energies in sequence and in a reciprocal or functionally dynamic manner generates a potential hexagram, in this way the system of application is inexhaustible. This does not mean that the essence of the I-Ching hexagrams is implied, as the essence of the Bagua trigrams is also not employed, indeed Peng is not heaven, Lu is not earth, however heaven an earth are reciprocal things, much as the energies are, and Peng is substantial or full while Lu is insubstantial or void. It does not mean that heaven figures into the application of Peng energy or that earth figures into the application of Lu energy, or that to use them in sequence generates a hexagram essence. It is a common misconception that Ji is water or an is fire, but Ji is not wet, nor is An hot, that has nothing at all to do with it. As those with formal teaching know long and short energies also play a role in this and with different energies the result of An is different, it can be used to push an opponent, but an opponent pushed does not have to be disconnected from and a push can displace an opponent and open them up to further attack. Moreover An can do serious damage and drop a person where they stand in other ways, though the energy is the same, the way it is manifested varies.
One way to understand this better is in regard to weapons applications, the energies are the same, but with a sword there is no push, no press etc, the energies do not change when one uses weapons, but the applications do. What is described in terms of the trigrams is thus not a philosophical or metaphysical system relating to the natures of the trigrams, but instead describes a complete system of movement and inherent methodology which accompanies it. One will also note that in terms of translation of the trigrams and hexagrams that there is some degree of variation that while problematic to philosophers and diviners has no impact upon the formal teaching of the 13 postures.
It may seem complex, but it is profoundly simple. One can more readily understand it that in a vital way, yang and yin do not exist as independent properties, but exist only in relation to one another. This is why the art is the martial system of taiji, it is not meant to be thought of in a grandiose and bragging sense of it being supreme or ultimate, it is meant to be understood in terms of how it is a complete and coherent system of functional and dynamic aspects based upon reciprocal energies. If one focuses too much upon the idea of the trigrams and hexagrams themselves they are very likely to miss the subtle and profound truth that is described in the use of the trigrams in regards to the 13 postures, it is all about energies, which can be felt, and not at all about the philosophy and interpretation of the trigrams as elemental forces. Actually, understanding this, as well as not understanding this is a sign of knowing and not knowing, of truth and not truth, in terms of taijiquan, it can show who knows the real art and who has an interpretative version. You don't find the truth much outside the formal transmissions, the 13 postures is a very specific martial method that has no room for loose interpretation or translation, and it can be taught without words at all, they are merely a tool to help teach the true martial art and in and of themselves are of no use whatsoever, knowing them is irrelevant to knowing the art and too much emphasis upon them often comes at the cost of preventing true understanding. It is better to have one true lesson in the physical art than to have ten thousand lessons in the words used in the art.