I know it's possible to change the
$ user@hostname colors, but is it possible to color different things? Could I make all numbers/integers a certain color. Or set certain keywords to be bold?
The coloring comes from the emission of various escape sequences. As such, they can only be reliably used when full control of the output is available, such as when outputting the prompt or when using specific programs.
Having said that, it is probably possible to write a terminal emulator that will do pattern-based highlighting, but I have never come across one myself.