There is a very good explanation (in Italian, but easy to read) here http://www.treccani.it/enciclopedia/raddoppiamento-sintattico_(La_grammatica_italiana)/
According to this source, we should double many consonants at the beginning of words while pronouncing them, and when such a word is written together with the previous word (as in sopra + tutto = soprattutto) the doubling is also reflected in spelling. The cause is the dropping in Italian of many consonants at the end of Latin words, and those consonants remain there to an extent at the beginning of the next word (e.g. a ccasa, tre ggatti, già ffatto). This is a very short summary of the page. For me, the information helps improve the pronunciation (I used to say a casa, tre gatti, etc, no doubling, which I now understand is wrong)
To me "we mostly talk... " and "we talk mostly ..." are almost the same.
"We mostly talk about animals" means, most of the time we talk about animals, but sometimes we go swimming and don't even talk. Do something completely different, not talking.
"We talk mostly about animals" means we talk about animals most times but sometimes we talk about food. But we always talk.
Not a big difference. Very subtle.
I'm not sure. "Above all" sounds more intense than "mainly". I wrote "especially" which sounds to me somewhere between "above all" and "mainly". I guess it depends if Italian also has similar levels of intensity. The Collins Italian-English dictionary gives "above all" and "especially" as translations of "soprattutto", and "principalmente" for "mainly".
Is word order important in this sentence, specifically as it relates to "sopratutto"? In English you can say "Mainly we speak about animals", "We mainly speak about animals", "We speak mainly about animals", "We speak about mainly animals", or "We speak about animals mainly" and they're all more or less correct, understood, and equal in meaning. Is it the same in Italian, or does "soppratutto" have a specific required placement in the sentence?
"Sopratutto" could probably go at the beginning of the sentence, but that's about it.
However, it's not that different in English. As you said, although some of your options would be understood in English, they're only "more or less" correct. Your last two options ("about mainly animals" and "about animals mainly") hit the ear wrong and shouldn't be offered as good translations.
You can't include "the" in the English sentence, because the Italian sentence clearly isn't referring to a definite set of animals. If the Italian sentence used "degli animali," then I think it could go either way; but since the Italian omits the article, the English version has to as well.