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1) Look at man statfs; the structure returned has both counts available (f_bfree and f_bavail).¹
man statfs
f_bfree
f_bavail
2) Yes, it works on filesystems, not hard drives, so it doesn't matter what type of hard drive (if any) the filesystem is on.
3) /
/
¹ In case the first part of the question was not about what statfs returns but what “the computer” displays in general, I guess the answer depends on the program used to display the amount of free space. Compare the two values returned by statfs to those displayed by the program you are interested in.
statfs