According to Mayo Clinic, Down syndrome causes a distinct facial appearance, intellectual disability, developmental delays, and may be associated with thyroid or heart disease in a person. So calling people with this syndrome 'Mongoloid' is extremely vulgar and disrespectful to ethnic Mongolians. Likewise, how will the population react if Down Syndrome was associated with 'European' looks? If you use this term, you are automatically a xenophobic, in my opinion.
An ERA is a long period of history with distinct characteristics. For example, the roman era. A PERIOD is less distinct and defined, it simply represents a portion of time, be it a very short portion, or a very long portion. For example, my period of sadness and the jurassic period. An EON is an actual unit of time. 1 eon = 1 billion years. This is also used rhetorically to symbolize a long long time. For example, man! my new iphone took like an eon to arrive in the mail! or also more appropriately the earth is 4.5 eons old.
Hyponyms (each of the following is a kind of era): day (an era of existence or influence) age; historic period (an era of history having some distinctive feature) modern era (the present or recent times)