Ludoviko was born in Bialystok, which wasn't part of Poland at the time. It was part of the Russian Empire, in the Grodno Governorate, as Ludoviko reported to Nikolai Borovko in a letter, which was was published in Lingvo Internacia in 1896: "Mi naskiĝis en Bjelostoko [Esperanto spelling based on Russian name], gubernio de Grodno."
Ludoviko was born in his parents' house on Ulica Żydowska (Jewish Street), though most biographies state Ulica Żielona (Green Street). We know that Ulica Żydowska was renamed Ulica Zamenhofa in 1919, and N. Z. Maimon has confirmed using maps of Bialystok that Ulica Żydowska is the same street as Ulica Zamenhofa, whereas Ulica Żielona was in a totally different part of town:
The biographies usually speak about a divided city with the Jews as a minority. That's not true. Pinkas Bialystok ("A Chronicle of Bialystok"), the "only work which we trust" according to the "Bjalistoker Center" in New York, gives the population in 1860 as 16,544, 11,288 (68.2%) of which were Jews. This rose to 76% by 1895. The other peoples of Bialystok were Polish, Russian, Germans, Belorussians, Tatars, Ukranians, Lithuanians, and more, each with their own languages and cultures.
Ludoviko didn't really think of himself as having a nationality so much as having an ethnic identity with an ancestral homeland. He called himself a "Jew from Russia", reflecting his birth in Bialystok, and thought of Lithuania (the Grand Duchy from the Middle Ages rather than the smaller country it became) as being his country of origin.
One thing he definitely wasn't, in spite of the mass of information claiming otherwise, was Polish. He wrote to the organisers of the 1912 Universala Kongreso in Krakow to tell them that they could promote him as "a son of Polish land" because it's in Poland where his parents are buried, where he works and intends to work until he dies, and it's where he lives, but they should not call him a Pole.
In a letter to his friend Alfred Michaux in 1905, Ludoviko said that he'd been top of the class all throughout high school. His high school certificate shows the grades he was accorded - the first score is what the teaching authorities awarded him, the second is the exam result:
Russian language and literature - 4 (good) - 4 (good)
Logic - 4 (good)
Latin - 4 (good) - 4 (good)
Greek - 4 (good) - 5 (excellent)
Mathematics - 4 (good) - 5 (excellent)
History - 4 (good) - 4 (good)
Geography - 4 (good)
German - 5 (excellent)
French - 5 (excellent)
Because of his grades he was awarded a silver medal, which allowed him access to any Russian university without having to go through an entrance exam.
Yiddish, which was the language spoken by the Jewish community where he lived. His father used Russian in the house, so Ludoviko grew up bilingual.
Yiddish and Russian were his domestic languages. He probably had familiarity with Hebrew because it was used in the synagogue.
He learned German and French from his father. German was the language that the Jews of the Enlightenment preferred to learn, and French was the international prestige language.
When he was 13 the family moved to Warsaw, where he learned Polish. At the grammar school there he learned Latin and Greek, and taught himself a bit of English. He was never good enough at English to be able to translate from it without using a German or Russian version as a parallel text, nor could write letters in it, but his exposure to it opened his eyes to the fact that a language didn't have to have complicated verb forms, grammatical gender or an abundance of cases.
There are suppositions that he had a smattering of Lithuanian and Italian but he doesn't appear to have commented on them himself.
Ludoviko trained to be a doctor. However, it became clear to him when he started working as one in Veisejai that he wasn't cut out for the job. He took it very personally when he couldn't help people, and the death of a small girl who he was unable to save traumatised him. He went back to university to retrain.
Ludoviko's birth certificate, being a formal document, was written in Russian, the state language. The name recorded for him, with cyrillic letters, is Eliezer, which was given to him during his circumcision. However, the formal name belongs only to religious life; in everyday circumstances, the Yiddish form Lejzer was used, and that's how the boy was known, with the diminutive Lutek available in particularly social circumstances. Upon moving to Warsaw, the Polish version Lazar came into use.
Since Bialystok was formally Russian, then his state name would've been the Russian version of Lejzer, plus the patronymic. His father was known as Mordeĥaj in Hebrew, and Motek, Mordka (as recorded on Ludoviko's birth certificate) and other forms in Yiddish, as well as Mark in Russian, giving the boy the official name Лазарь Маркович Заменгоф; Lazarj Markovich Zamenhof. Indeed, that's the name we see on his formal education papers and which he occasionally signed in his early Esperanto correspondence.
Ludoviko's brother Leono became a doctor in 1900. Since Leono was an Esperantist too, Ludoviko started using the form Dr L. L. Zamenhof to distinguish himself from the other Dr L. Zamenhof.
Ludoviko was conscious that his professional reputation might suffer if his real name appeared attached to a new language, so he chose to hide it. He called himself "Doktoro Esperanto", which meant "the hopeful doctor". Some Zamenhof specialists suggest that he also chose it as a play on words, since his surname was original German and hoffen in that language means hope, although Ludoviko isn't known to have stated this.
He didn't. The published version of the language was simply called Lingvo Internacia (International Language). When referring to it, his predominantly Russian audience would refer to it as "the Language of Esperanto", in order to distinguish it from other language, and usage quickly shortened it down to a single word.
The most obvious pseudonym was Doktoro Esperanto, the name he used when publishing the language. There were at least nine others that he was known to have used: Amiko, D-ro X., N.N., Hamzefon, Hemza, Homo sum, Homarano, Unuel, Anna R.
He also once wrote an "open letter to sinjoro de Beaufront" in Ruslanda Esperantisto in which he hid behind the name of Aleksander Naumann, who was a known Russian Esperantist.
This is very much a work in progress and will eventually contain many more sections and questions!