According to https://en.wiktionary.org/wiki/estro#Esperanto, "estro" is a "Back-formation from -estro ('leader')." And according to https://en.wiktionary.org/wiki/-estro#Esperanto, the suffix "-estro" is "Perhaps from the endings of Italian maestro, German Meister and Bürgermeister, and French bourgmestre."
According to https://en.wiktionary.org/wiki/edzo, "edzo" is a "Back-formation from edzino, less the feminine suffix -ino.", and according to https://en.wiktionary.org/wiki/edzino#Esperanto, "edzino" is "Perhaps back-formation from Yiddish רביצין (rebetsin, 'rebbetzin, rabbi's wife'). Zamenhof's explanation that it was from German Kronprinzessin ('Crown Princess') is thought to have been an attempt to avoid antisemitism."
But I'm not sure, in how far these pieces of information are right.
estro is a generic suffixe for all kind of people with power over something or someone: of a ship, an office, a hotel, a province, town or village, a kingdom, an army or just 100 soldiers, some workers, officers or engineers. See http://vortaro.net/#estro
So manager is on of its translations
It is not correct word order in English. Esperanto has a more flexible word order. In English you may say "We like our boss a lot" or "We very much like our boss" but you may not break up the verb - object in the sentence as in "we like a lot our boss". So content is totally ok but word order is not.