It's somewhat random but if you slay enough monsters, and collect a lot of materials it'll increase the odds as the game eventually has to reset all that to clear up memory.
Once you have the parachute the whole of Hyrule can be accessed. Though you may need something to protect you from the harsher climates.
The in game map is the same as the interactive map. You just need to fill it in by activating the towers. Again the entirety of Hyrule is open.
Nope
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