How the ideas connect
A good science page should make the connection visible, not just list definitions.
Enthalpy
Enthalpy is a thermodynamic state function. At constant pressure, under the usual conditions for pressure-volume work, its change is especially useful for discussing heat transferred.
A negative reaction enthalpy is associated with an exothermic process under those conditions; a positive value with an endothermic one.
Entropy
Entropy is a thermodynamic state function connected to the number and distribution of accessible microscopic states and to energy dispersal.
The slogan “entropy equals disorder” can be misleading; statistical and thermodynamic definitions are more precise.
Gibbs energy
At constant temperature and pressure, Gibbs energy provides a criterion for the direction of spontaneous change in a closed system under the usual constraints.
A negative ΔG indicates thermodynamic favourability for the specified change, but says nothing by itself about how fast it will happen.
Conservation of energy
Energy can move between stores and cross a system boundary, but for an isolated system total energy is conserved.
Thinking in terms of energy often lets us solve a problem without following every detail of the motion.
What to notice
A good science page should make the connection visible, not just list definitions.
Sources
IUPAC Gold Book · NIST · BIPM