I don't think there's any detailed information available about what each of them did during their time in Australia, and I'm certain that all of the specific characters and events depicted there are fictitious (in fact, in real life they weren't all sent to Botany Bay: George Loveless was sent to Van Diemen's Land (Tasmania), perhaps to ensure that, as the leader, he was separated from the others). However, it is true that Hammett could not immediately be located when news of their release came through, and came back later, separately from the others.
This relatively blank historical canvas gave Bill Douglas a wonderful opportunity for inventiveness, but the structure he creates in this half of the film is straightforward: there are six segments, one for each of the martyrs, in the order George L, Brine, Old Stanfield, Young Stanfield, James L, and finally Hammett. What work they are actually assigned isn't as important, and as you say in a couple of cases isn't even mentioned: it's the ideas and character that each portrays during his sequence that is important, and the fact that each in turn has a chance to emerge as an individual.
Until they are reunited at the end (and Hammett not even then) the six main characters don't see each other all the time they are in Australia, but Charlie meets four of them, so he's a linking device that helps bind the sequences together (I think it's significant that he doesn't appear in all six segments, because Douglas wouldn't have wanted to make the linking too obvious and heavy-handed). The fact that he doesn't realize that they know each other contributes to the sense of anonymity and alienation that must have been an integral part of the dehumanizing experience of being a transported prisoner.
Charlie doesn't inveigle his way into the governor's mansion: it's the destination he was assigned to and to which Mrs Carlyle took him. He isn't meant to be "disguised" as an aboriginal: it's a costume his employer gave him, at a time when having domestic servants from "exotic" backgrounds was fashionable. After the orange grove sequence he's captured by the wealthy man, who then adopts him, perhaps with the idea of making him his heir (in both cases the men are trying to change Charlie into something he's not, as if he were clay they could mould as they wished). Hammett would have realized that Charlie was a convict as soon as Charlie opened his mouth (presumably some time before the scene we see) and heard that there was no posh accent to match his posh clothes.
By the way, I think Hammett's speech in this scene is emotionally, politically, and morally the high point of the film: if you want a distillation of what the whole thing is about in a few sentences, this is it.
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