Look at the panel
properties to change the Problems panel.
"workbench.colorCustomizations": {
"panel.background": "#0b698f",
"panel.border": "#ff510060"
}
But it will change the background for all the panel items, like Terminal, Problems, Debug Console, etc.
You can override that setting for the Terminal only:
"terminal.background": "#ff0000",
It would appear that the Problems panel fontFamily cannot be independently set as I see only these two panel fontFamily properties:
"terminal.integrated.fontFamily"
"debug.console.fontFamily"
You might be able to figure out how to do it with the Custom CSS and JS extension. See, for example, How to change the font in VS Code's 'Explorer' window?
Maybe it is <div class="composite panel markers-panel"