Yes, It doesn't madder what direction you name them unless you were given specific instructions.
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Yes it names the same ray. For example in a square ABCD you can also call it DCBA or BCDA etc.
Yes.
According to the symmetric property (and common sense) line segmetn AB is congruet to line segment BA since they are the same segment, just with a different name
Line BA
If these are vectors, then ba = - ab