Are negative vectors unlike parallel vectors?

Yes, negative vectors are unlike parallel vectors.

Parallel vectors may or may not be of the same magnitude. But, a negative vector is of the same magnitude. 
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Comment on the statement: Like parallel vectors are equal vectors.


The statement is wrong because like parallel vectors need not have equal magnitude while equal vectors have equal magnitude. 
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Can two non-coplanar vectors be parallel vectors?

No, coplanar vectors cannot be paralle vectors as they are intersecting vactors. 
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What changes take place in the vector when it is replaced parallel to itself without changing its magnitude and direction?

When the vector is replaced parallel to itself without changing it's magnitude and direction, the vector remains unchanged.
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Are unlike parallel vectors negative vectors?

No, unlike vectors and negative vectors are different vectors. Unlike parallel vectors need not have equal magnitude. 
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