If you google quando eu era criança/uma criança and quando eu fui criança/uma criança you’ll see that era beats fui 210 to 1. This is partly because quando eu era (uma) criança is more idiomatic, but that’s not all.
The first thing to note is that the absolute length of time an action or state lasts is a rather poor guide to choose between era (pretérito imperfeito, PImp from now on) and fui, foi (pretérito perfeito, PPerf from now on). Compare:
(a) Frank Sinatra foi um dos cantores mais famosos do século XX. (Frank Sinatra was one of the most famous singers of the twentieth century.)
(b) Frank Sinatra era um bebé de dez meses quando os Estados Unidos reelegeram o Presidente Woodrow Wilson. (Frank Sinatra was a ten-month-old baby when the United States re-elected President Woodrow Wilson.)
See, Sinatra was a famous singer for decades, but we used the PPerf in (a). And he was a ten-month-old baby for a month only, but we used the PImp in (b). So forget about length of time! What really matters is that is that the PPerf indicates a complete action or state, and the PImp indicates an incomplete action or state.
The state of Sinatra’s being a ten-month-old baby was not complete when Wilson was re-elected on November the 7th 1916: it had started earlier, on October the 12th, and continued afterwards for four more days. That’s why we used PImp in (b). But the state of Sinatra’s being a singer was fully complete in the twentieth century. His whole life was. That’s why we use PPerf in (a).
Now, getting back to childhood:
(c) Visitei a Itália com os meus avós quando era criança. (I visited Italy with my grandparents when I was a child.)
(d) Vivi dois anos no Brasil quando era criança. (I lived in Brazil for two years when I was a child.)
(e) “Mãe, és má. Não sabes o que é ser criança.” ─ “Claro que sei: eu também fui criança.” (“You’re a bad mom. You don’t know what it’s like to be a child.” ─ “Of course I know: I was a child too.”)
(f) Eu fui criança em tempos muito difíceis. (I was a child in rather hard times.)
In (c) there is a complete action, visiting Italy, as indicated by the PPerf visitei. Of course you were a child before, during, and after the visit to Italy, so you use the PImp era to indicate that being a child was not complete when you visited Italy. The same is true in (d) about living two years in Brazil. In (e) the mother refers to her entire childhood as a complete state in the past, hence the PPerf fui. In (f) too, the speaker refers to his entire childhood, which took place during hard times.
Now, (e) and (f) could be rephrased with era:
(e1) “Claro que sei: houve um tempo em que também eu era criança.” (“Of course I know: there was a time when I was a child too”. The original (e) is more natural.)
(f1) Quando eu era criança, os tempos eram muito difíceis. (When I was a child times were very hard.)
The information conveyed in (e) and (e1) is the same, as is that conveyed in (f) and (f1). The only difference is the frame of mind: in (e) and (f) you see your entire childhood in the past from a point of view in the present; whereas in (e1) and (f1) you see your childhood as an ongoing process from a point of view in the past during your childhood.
For some reason not entirely clear to me quando coupled with being a child appears to elicit the ‘ongoing-process-seen-from-a-point-of-view-in-the-past’ frame of mind, which requires PImp. Maybe that’s because the boundaries of childhood are a bit fuzzy (there isn’t a precise moment when you stop being a child) and quando + PPerf suggest a period with clear beginning and end. So you say:
(g) Quando eu era criança, gostava de ler contos de fadas. (When I was a child I enjoyed reading fairy tales.)
(h) Quando era criança, detestava couves. (When I was a child I hated cabbage.)
(i) Quando eu era criança não havia iPads. (When I was a child there were no iPads.)
(j) Viajava muito quando era criança. (I travelled a lot when I was a child.)
Of the above the only one that sounds fine to me with fui in place of era is:
(i1) Quando eu fui criança não havia iPads. (When I was a child there were no iPads.)
In (i1) one can easily imagine one’s entire childhood within a longer spell of time when the iPad had not yet been invented. When we’re talking of a state with clear beginning and end, as being sergeant in the army below, quando + PPerf becomes natural, although the PImp is be fine too:
(k) Viajei muito quando fui/era sargento no Exército. (I travelled a lot when I was a sergeant in the Army.)
When you´re talking about past events and have no time markers you’re usually free to adopt the frame of mind you like: whole event seen from the present (PPerf), or ongoing process seen from a moment in the past during that process (PImp):
(l) O t-rex foi/era um animal perigoso. (T-rex was a dangerous animal.)
(m) Eu fui/era uma criança brincalhona. (I was a playful child.)
(n) Einstein foi/era um cientista. (Einstein was a scientist.)
Time markers may elicit PPerf only or PImp only:
(l1) O t-rex foi o maior carnívoro terrestre de todos os tempos. (T-rex was the largest land carnivore of all time. His all existence is included in all time, hence the PPerf.)
(l2) Aquando da grande extinção do final de Cretácio, o t-rex era o maior dos carnívoros terrestres. (At the time of the great late-Cretaceou extinction, t-rext was the largest of land carnivores.)
(l3) Até à sua extinção, o t-rex foi o maior dos carnívoros terrestres. (Until it went extinct t-rext was the largest of land carnivores.)
(l4) Antes da sua extinção, o t-rex era o maior dos carnívoros terrestres (Before it went extinct t-rex was the largest of land carnivores.)
(n1) Aos trinta anos, Einstein já era um cientista famoso. (At the age of thirty Einstein was a famous scientist already.)
Now, how best to translate Einstein was a jew is complicated. Consider the following:
(o) “Quem foi Einstein?” – “Einstein foi um cientista.” (“Who was Einstein?” – “Einstein was a scientist.”)
(p) “Quem foi Einstein?” – “Einstein foi um judeu.” (“Who was Einstein?” – “Einstein was a Jew.”)
(q) “Einstein era Alemão?!” – “Foi até 1933. Einstein era judeu, e abdicou da cidadania alemã em 1933” (“Einstein was German?!” – “He was until 1933. Einstein was Jewish/a Jew, and renounced German citizenship in 1933.”)
Foi um + noun, as foi um cientista or foi um judeu, is more about essence, usually an answer to who was? So answer (o), a scientist is more natural than (p), a Jew, unless you’re obsessed with race or Jews. There's a somewhat related discussion in SE.ELU. When asking who was, quem foi is more common than quem era, but both are possible.
Era + adjective is more about describing someone when you already know who they are. Hence era alemão and era judeu in (q). In Portuguese many words are both nouns and adjectives, but you usually can tell a noun because of the um or uma. Foi até 1933 because até 1933 includes all time till 1933, so then the state of his being German was complete.
And to conclude see how just by substituting fui for era can sometimes change the meaning of a sentence. When you buy a car visit several dealers, let them know you’re doing so, and you’ll get a lower price. But when I bought my first car I visited one dealer only and paid the price they asked. The possible explanations for this are that:
(r) Eu era muito ingénuo. (I was very naïve back in those days.)
(s) Eu fui muito ingénuo. (I was very naïve on that particular occasion.)
