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Not every relation is a function. But every function is a relation. Function is just a part of relation.
Horizonatal line test is a test use to determine if a function is one-to-one. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one. A one-to-one function is a function where every element of the range correspons to exactly one element of the domain. Vertical line test is a test used to determine if a function is a function or relation. If you can put a vertical line through graph and it only hits the graph once, then it is a function. If it hits more than once, then it is a relation.
One way is to try the vertical line test on a graph!
A function is a relation whose mapping is a bijection.
No. A relation is not a special type of function.