Everyone of your questions can be answered with a "Maybe".

Bachmann factory installed decoders are called "Sound Value" decoders.  even though they are made by SoundTraxx, there have reduced functionality compared to regular SoundTraxx sound decoders. This may not be true for other manufacturers -- I am not aware of any LokSound decoders installed having reduced capabilities.

Most sound are recorded by the manufacturer from an actual model of the real loco.

Some aftermarket sound decoders come with preinstalled sounds. Other like LokSound can provide blank decoders and the modeler or the dealer installs the sound file from a very large library of sounds for particular loco.

Factory fit decoders can come with either generic or specific sounds. You will have to determine that for yourself based on the loco manufacturer and the decoder manufacturer.

Sometimes the sounds on factory fit decoders be replaced -- e.g. Digitrax, LokSound.

Hope this helps