The VT100 terminal codes support setting the current color, and a "reset to default" which resets the color (and other attributes) to whatever the terminal considers the defaults. VT100 is the normal "baseline standard" that most commands support, though some might be programmed to be aware of more advanced terminal capabilities.
I am not aware of any way to change the color that the terminal considers the default, from within the terminal. This might be possible using i.e. some gnome command line tool to reach into the gnome settings system and change it for gnome terminal, but that might affect your entire window and not just the next to-be-written lines, and it would be very specific to one desktop arrangement.
You can easily change the current color inbetween commands, though. Your shell (like bash - see "PROMPT_COMMAND" ) usually has a way to run arbitrarily complicated code when rendering the prompt. But, if the command you run starts to alter the color of the terminal, there's probably no way to change it back to what you wanted until the end of the command. So that red "Error:" text in your example will change the rest of the color of the output until the next prompt. There might be some way to filter the output of all programs you run, but that would be asking for trouble down the road.
Also, those custom pink/blue aren't standard colors, so you'd have to research how to do that with the terminal you are using. (maybe update the question with that?) Otherwise here are the standard VT100 colors