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No, algebra 1 is defiantly not the same as math course 3.
yes you would have to because that would be the full course of algebra just at a slower and easier pace
Yes, the great Mrs. Mazz said that algebra 1 is a quite rigorous course it requires a great deal of thought and perseverence.
foundations algebra is probably pre algebra, which is before algebra, so no.
Probably not much; of course you'll learn new things (just as you did in algebra), but they will be introduced gradually (just as they were in algebra).