"Where are you?" translated as "вы где?" "Where are they?" translated as "где они?"
Is the word order important here? The notes mention a little bit, but I am unsure. Thanks.
In Russian most of the time you can rotate words in a sentence without changing its meaning. People will understand you, but sometimes some combinations sound a bit strange or funny, or even a bit wrong. In this case, there is no real difference where you put "где", but "Где они?" sounds more natural to me than "Они где?". Although, "Где вы?" is the same as "Вы где?" to my ear.
No, in Russian things are just "plural", the gender becomes irrelevant. So они is just "they", like in English.
"Они" means "they", this word it's for both genders? Or they have another word (like in latin languages)?
"She" = "она." And for completeness:
"he" = "он"
"it" = "оно" (Sort of. The nominative pronoun for neuter singular at any rate.)
"they" = "они"
It's like in English, it can refer to a group of people or to a group of inanimate objects as a substitute for the full noun.
So, here some basic examples of when you would use the verb "be" in Russian. For every day speech it is omitted from sentences.
1) Past Tense: If something "was", you would conjugate the verb быть in the past tense (был, была, было, были). (Где они были? = "Where were they?")
2) Future Tense + imperfective verb: to indicate an action that will be continuing or repeating in the future, or to say simply "will be". Они будут там = "they will be there". // В школе будут проводить уроки по четвергам = "Lessons will be conducted on Thursdays at the school".
3) As a participle ("being") that can be used in a sentence with any tense - Будучи неопытными, они делали много ошибок - "Being inexperienced, they made a lot of mistakes", but this is more literary and in spoken Russian or simpler news reports you'd more likely see "Так как они были неопытными..." or "Так как они - неопытные..." (past, present).
4) As an imperative (command) - Будь внимателен! - Pay attention (or Be careful!). // Будьте там в шесть! - Be there at six!
5) There is one other word - являться - that basically means "to be". This is a higher level word that you will only hear in formal speeches or technical texts, presumably to make concepts more straightforward. Дерево является растением - A tree is a plant. Note that it takes instrumental case.
SO... TL;DR - Only in the present tense can you really get away without the verb "to be".