1) Yes, that was clearly supposed to be Max. He's framed the exact same way as in the beginning of Fury Road.
2) It's just a case of poetic revenge. He killed her mother and stole her away from the Green Place because he was looking for it and in death, she brings part of The Green Place to him. One thing to note is that all Mad Max films, and especially this one, are more mythological than literal, so it makes sense she would "kill" him like this.
3) Probably figured correctly that running away as a child would get her killed or raped very fast. While staying at the Citadel could provide opportunities.
4) Not sure, could be, but I think it's new footage (and not Theron)
As for your question regarding the Mad Max franchise. None of the Mad Max films are reboots (as Max Rockatansky is always clearly the same guy, even in Fury Road he mentions his background from the first movie), but also none of them are direct continuations of each other.
The Mad Max films, except the first one, are more like tales people tell in the future about this mythical figure called Max who helped their society at one point (or in this movie, the myth about Furiosa's rise). The stories are not really meant to be taken literal, which is why you get stuff like the Wasteland looking completely different with each movie, the timeline completely shifting and Max himself being seemingly ageless (in Fury Road for example, he would've been several decades older than most other characters in the movie).
Furiosa is the first Mad Max movie that is explicitly set in the same kind of story-environment as a previous film (Fury Road) and even then you can see differences in how the characters acts between stories (most obvious with Rictus and Immortan Joe).