Yes. It forms the basis for any higher mathematics. Success in science depends upon ones knowledge of algebra and other higher mathematics.
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Algebra exists to find solutions
Islamic algebra is the same as regular algebra. just like Arabic numerals is the same as 1 2 3. why is algebra important today? there is no difference between these questions.
He did not really come up with algebra: he put together the thinking behind algebra in one book.
Algebra was not an important invention to Islam as a religion. It was an important invention in mathematics that was discovered by a Muslim (Al-Khwarizmi). Algebra is important in mathematics because it establishes the ability to perform mathematical operations even if some or all of the quantities are unknown.
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.