That is often called the magnitude.
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No. The size of the size of the vector drawn indicates the magnitude.
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
another displacement
It is a vector with the same magnitude (size) but acting in the opposite direction.
There does not seem to be an under vector room, but there is vector space. Vector space is a structure that is formed by a collection of vectors. This is a term in mathematics.