Ah well, at least you now know what is happening !
To find out if you can permanently set the printer to colour you are going to have to plough through the printer options, or just get into the habit of checking the printer settings when you use Foxit.
I have a Canon printer and if I want to print in gray scale - as I do from time to time - then if I set it to gray scale it stays that way until either I change it back to colour or close the application and open a different application, then it reverts to the default which is colour.
Not all applications support keystroke combinations, which is probably why Foxit doesn't respond to 'Ctrl+P'. In general, from my experience, clicking the printer icon on the menu bar sends a job to the printer with default settings and you don''t see the printer panel. Clicking 'File / Print' normally brings up the printer screen so you can control the printing.