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1. When does one chapter end and another begin? Are there some key events I need to trigger or does it just change with the cycles? Because I feel like I've been in the Confusion chapter for too long and I'm just wasting time harvesting and opening up places when i should be doing _something_.
It is all about time. The idea is roughly the same as is Pathologic: the world doesn't care what you do. Chapters change with time - and yes, "Confusion" is quite long. The end of the game is just after 35:00, and if you get youself to that point, you are surely to get an ending. Getting the ending you want, on the other hand, will require some work.
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2. The Brothers are starting to get really aggressive, which further leads me to believe I've upset them somehow. I've tried to do whatever tasks they asked me but really got no feedback from them (aside from the fact that I didn't end up in an arena with Mantid in cycle 10 like some people have).
There are no tasks, as far as I remember, aside from those from Whaler, Mantid and Warden. Surely you can visit Mantid for a feedback, but generally you don't have to report the tasks done. The brothers don's actually give any reward, just "are quite pleased" and don't attack you.
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3. I've managed to kill the 3 "worms" and still got no reward (as I was promised), instead I received a challenge from a random Brother to fight him (at about 23:50 or so).
These are not related. Mongolfier rewards you with "Wasp", if it wasn't changed before the English version was released. I suppose, you already have this glyphs.
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4. Can I just stay "out of trouble" so to speak? Not get into any Brother fights, just mind my own business and do their tasks if they ask me to? Or do I _have_ to fight some of them to finish the game?
No, you can't. Later in the game several brothers who don't trust you fight you no matter what. Three (or two) will. And one more, maybe... I'm not sure about the English release version. There were four fights in the original, but we may have removed one, because it didn't look neither particularly interesting, nor surprising to me...
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5. Can you find all 20+1 Hearts in the chambers? Or do I absolutely have to fight some Brothers for that?
You are sure to get the last one when the story wants you to; so you can't find this one on your own. As for the rest of the hearts... some of the fights are inevitable. But if you search in the chambers well, then you won't need to fight more brothers than fight you of their own will. If you miss some hearts in the chambers, OK, then you will need to fight some more brothers and get hearts after their death. Anyway, by 29 or 30 cycle you can have 20 already. Nothing prevents you from it.
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They're starting to attack me every cycle starting at about 24-25, is there anything I can do to avoid this?
I am pretty sure they shouldn't. Perhaps you give much colour to the Sisters. If you open the third heart of a Sister, then the corresponding Brother is going to fight you.