>> Far less chances of getting injuries with bodyweight exercises
> I found no evidence for this,
From Wikipedia:
"""
Bodyweight exercises have a far lower risk of injury compared to using free weights and machines due to the absence of an external load that is placing strain on the muscles that they may or may not be able to deal with. However, the lower risk of injury is only provided that the athlete/trainee is progressing through the correct progressions and not immediately skipping to strenuous movements that can place undue and possibly harmful stress on ligaments, tendons, and other tissues. Although falling on the head, chest, buttocks, and falling backwards can occur, these are far less harmful injuries than dropping a weight on a body part, or having a joint extended beyond its natural range of motion due to a weight being used incorrectly.
"""
That quote makes no sense. Load on the muscle is there with both bodyweight and weighted exercises - that's how you train the muscles. And the caveat about not skipping progressions works just as well for weighted exercises - you progress gradually so you never produce "strain on the muscles that they may or may not be able to deal with".
The quote actually addresses the rest of your points pertaining to calisthenics (correct progression, with good form, is important; those who "rush" are likely to get injured regardless of weights).
> I found no evidence for this,
From Wikipedia:
""" Bodyweight exercises have a far lower risk of injury compared to using free weights and machines due to the absence of an external load that is placing strain on the muscles that they may or may not be able to deal with. However, the lower risk of injury is only provided that the athlete/trainee is progressing through the correct progressions and not immediately skipping to strenuous movements that can place undue and possibly harmful stress on ligaments, tendons, and other tissues. Although falling on the head, chest, buttocks, and falling backwards can occur, these are far less harmful injuries than dropping a weight on a body part, or having a joint extended beyond its natural range of motion due to a weight being used incorrectly. """