Calculate enthalpy change in reactions.
Because enthalpy is a state function, the enthalpy change of a reaction depends only on the initial and final states — not the route between them. That is Hess's law, and it means the reaction enthalpy is the summed standard formation enthalpies of the products minus those of the reactants, each already weighted by its stoichiometric coefficient. Elements in their standard state have a formation enthalpy of zero by definition.
Hess's law
delta H reaction = sum delta Hf(products) - sum delta Hf(reactants); energy released = delta H x moles reacted
Yes, before entering them. Burning methane produces one CO2 at -393.5 and two H2O at -285.8 each, so the product sum is -965.1 kJ, not -679.3.
By convention, an element in its most stable form at standard conditions has zero formation enthalpy. O2 gas, graphite carbon and N2 gas are all defined as zero, which is what makes the differences meaningful.
Not necessarily. Spontaneity is governed by Gibbs free energy, which also includes entropy and temperature, and even a strongly exothermic reaction can be blocked by a high activation barrier — a mixture of hydrogen and oxygen sits stable until ignited.