Either define finite first (usually as equivalent to a set of the form {1,2,3,...,n} for an integer n, in which case infinite is not finite; or use a set is infinite if and only if it is equivalent to a proper subset of itself. Equivalent sets A and B are those for which there is a function f taking A into B which is bijective (one-to-one and onto).
For example, the positive integers are infinite because we have the pairing: 1 -> 2, 2 -> 4, 3-> 6, ..., n -> 2n, ...; so {1,2,3,...} is equivalent to its subset {2,4,6,...}
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In general, the plane is infinite in length and breadth and so infinite in area.
An infinite amount because there are an infinite amount of numbers that you can keep adding to.
Infinite means that no matter how high or low the magnintude of your answer is, it will always be correct.
An infinite flat surface, or an infinite surface with zero curvature.
There is no highest math. The Complexity can be infinite. There is also a ton of math that hasn't been discovered yet.