Is there a standard length of margin left that works for all printers? On my note taking app I want to know how much space to leave so that when I export to PDF and print (on HP, Brother, Epson, you name it) none of the text is left out.
There is no standard.
If this is intended for office printing, I might be wrong but I don't think it matters much, as you can always check the 'Fit to Page' scaling option, which will auto-adjust the pages based on your particular printer and its particular margin settings.
I would use a minimum value between 5-8 mm and print with 'Fit to Page'.
No, there is not.
I have seen printers that leave only like 2 mm as borders, and some that need like 1.2 cm.
There are laser printers, inkjet, etc. (there are a LOT of options). The biggest margin is generally the bottom one.
I would say that you need to learn how to interact with the printer. There are several applications that ask for the printer's declared margins. Try Adobe Reader as an example.
When you send something to print, you have the option to send in real size or to scale to fit. I am assuming the scale to fit takes some information about the printer and uses it as a reference.