There are problems with at least THREE of these statements. However, part E) is DEFINITELY UNTRUE.
A) While Einstein assumed that light travels at a finite and constant speed c in a vacuum, he didn't assign any particular value to c, understanding that its value is subject to experimental verification. It was in fact known at the time both more accurately than 3 x 10^8m/s, but far less well than to 9 significant figures! So, because of the specificity of part A), it is in fact NOT TRUE.
C) should say "... at a speed equal or greater than that of light IN A VACUUM." (When particles travel at speeds greater than that of light in some given MEDIUM, "shock waves" of light called Cerenkov radiation are emitted. They are the analogue of sonic booms in air.)
E) is simply gobbledygook, and does not make sense as it stands. In fact as Einstein showed, the "effective mass" for a moving particle of rest mass mo (in a given rest frame) is
m_eff = mo / [sqrt (1 - v^2 / c^2)]. The energy equivalent of this, m_eff c^2, is LARGER than mo c^2 by an amount which reduces to the classical kinetic energy, 1/2 m0 v^2, at low speeds (low in comparison to c). Athigher speeds its mathematical form naturally changes. The difference between m_eff c^2 and mo c^2 can be thought of as providing a quantity we can define as "kinetic energy" at all speeds. However, that doesn't really help serve any other purpose. Physicists applying relativistic concepts to analyse the results of high energy experiments tend to use the total energy in their analyses, rather than "splitting off" the two separate parts. (There are however some "threshold" considerations where one could argue that it still plays a useful role.)
In any case, the "gain in internal energy" is part of the increased effective mass of the particle due to it being in motion. It does NOT come at the expense of the particle LOSING its mass or mass-energy, but rather as a result of the latter being INCREASED by whatever accelerative forces are acting on it.
So part E) is the answer that is DEFINITELY WRONG, while other parts are only perhaps rather flawed statements that can be expressed more accurately.
Incidentally, despite what some responders have said, part D) is certainly TRUE. The energy of chemical explosions or indeed the non-explosive heat generated in some chemical experiments comes from a change in the binding energy of electron clouds in the atoms and/or molecules involved. These effects are analogous to the changes in nuclear binding energies involved in nuclear explosions. Both are subject to Einstein's celebrated relation
ΔE = Δm c^2.
The great, indeed dramatic difference in their effects is attributable to the fact that the binding energies of the electrons in atoms and molecules are of order eV, whereas those of the nucleons are of order MeV, a million times greater!
Live long and prosper.