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I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
No, but they are examples of linear functions.
There are infinitely many types of functions. For example: Discrete function, Continuous functions, Differentiable functions, Monotonic functions, Odd functions, Even functions, Invertible functions. Another way of classifying them gives: Logarithmic functions, Inverse functions, Algebraic functions, Trigonometric functions, Exponential functions, Hyperbolic functions.
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You can evaluate functions at points. For example, my pay is a function of how many hours I work. At 5 hours I can evaluate the result.