Hot answers tagged internally-geared-hub
This picture shows a slightly better angle. You need to first loosen the lock nut slightly, then spin the adjuster barrel until it unscrews right off the threaded rod on the chain. When you re-assemble you reverse that, and have to re-adjust the tension so that it shifts properly.
Old, plain, one-gear Velosteel-like hubs had this feature thanks to using rollers instead of cogs, but I suppose it does not meet your expectations. If you REALLY need this feature you can modify Shimano Nexus 3 to obtain what you want by removing four cogs from part no 4 shownhere. You will lose 1st gear, rest will work as before.
It is normal - cogs of 1st gear turn slower than that from 2nd and 3rd gear, so are overrun and click into hub housing. You can "silent" it a bit by opening the hub and greasing hub housing, where the cogs work.
To the last question, a far better order of doing things would have been to disconnect the shifting cable first. The knurled part at the end of cable rotates on the threaded piece at the end of the chain, visible through the hole in the wheel nut. Rotate it to disconnect the cable.
While using IGH hub it's good to learn pedal repositioning technique different from freewheel hub. You may observed that when bike is pushed backwards, the pedals also go backwards. Of course, at junction there is not enough distance to go back enough to lift your favourite pedal to position convenient for start. But you really need centimetres-long distance ...
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