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Geometry is like a block from Algebra 1 to Algebra 2 and it contributes by teaching you the basics of the things you will learn in Algebra 2.
Pre-algebra is where you just learn the basics of Algebra and Algebra two is way more advanced with new information and taking the concepts you learned in pre-algebra and algebra to the next level.
It isn't; the algebra 1 and 2 that you get taught in middle or high school is elementary algebra. When (if you want to) you get into more advanced algebra, you can learn linear algebra (matrix algebra) and abstract algebra (which involves sets, operations on sets, groups, and many more concepts), and probably several more types of algebra I've never heard of.
Mainly algebra.
Yes. Definitely.