This is overly simplistic and objectively untrue; for example the PVC handle on my vacuum cleaner glued very well using solvent pipe cement
It massively depends on the plastic. Thermosets may respond well to glueing but which is the best glue will vary depending on the type of plastic. Thermosoftening plastic variants typically respond well to welding with a compatible material
There is no one thing called “plastic”, so no one answer fits all
Keitai for your Velcro I would replace it as suggested. For the headphones I’d probably brace the joint with a shaped metal plate, carefully screwed on with small screws, like what the hospital would do if you smashed a bone..
..but unless they’re audiophile grade, I’d probably just replace them as time wise a repair can rapidly outweigh the cost of a new pair
Yes because inhaling burning plastic fumes is everyone’s idea of a fun Friday night. Consider the neighbours please, and take it for recycling instead