No. College Algebra and Precalculus (or Trigonometry) are enough preparation to take Calculus.
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Most of the time, you don't use calculus or other types of advanced math in your daily life, unless "daily life" specifically involves working in some engineering branch, teaching advanced math, or something similar.
Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.
algebra, alg II, geometry, geometry II.
Yes. I use them a lot when answering these questions.
Not much. In any case, you won't need advanced math (like trigonometry, algebra, calculus, logarithms...) which you only use in science and engineering careers.