Does an orbital with the electron address of 3, 1, -2, 1/2 actually exist? Why or why not?

apple2017-05-31T07:09:21Z

NO
the first number shows that n=3
second number shows that subshell is p (L=1)
subshell p can have -1, 0 and 1 as mL(-L<=ml<=L) but the third number is -2,p subshell doesn't have such ml

supastremph2017-05-31T06:40:56Z

No, assuming you're listing them as n, l, m, because m can only run to +-l. and -2 is less than -1.