Short answers, pulled from the story.
The United States Centers for Disease Control and Prevention defines epidemic as an increase, often sudden, in the number of cases of a disease above what is normally expected in that population in that area. The term "outbreak" can also apply but is usually restricted to smaller events.
An epidemic may be restricted to one location or country, while a pandemic refers to an epidemic that has spread to other countries or continents and affects a substantial number of people across those regions.
A factor that contributed to the initial rapid increase in the 2014 Ebola virus epidemic was the ritual bathing of infective corpses. One of the control measures that helped contain the outbreak was an education campaign to change behavior around funeral rites.
Antigenic drift is a gradual process in which mutations accumulate in virus genes over time across a series of hosts, eventually producing a new strain that can evade existing immunity. Antigenic shift is abrupt: two or more different strains coinfect a single host, combine, and form a new subtype with a mixture of characteristics from the original strains.
The term epidemic derives from a word form attributed to Homer's Odyssey and later took its medical meaning from the Epidemics, a treatise by Hippocrates. Before Hippocrates, related forms of the word had meanings closer to "indigenous" or "endemic" rather than referring to rapid disease spread.
The 1854 Broad Street cholera outbreak is regarded as the foundation of the science of epidemiology. A cholera epidemic was mitigated by identifying and removing a supply of contaminated water, establishing the principle of tracing disease to its source rather than treating symptoms alone.