I'm so confused about avogadro's number.
How were scientists able to change from oxygen and hydrogen to Carbon-12? Couldn't any number be avo's number, why did they choose 6.02 etc.
I don't think oxygen was ever part of the definition. It was definitely used as a part of the relative atomic mass definition, perhaps you mixed these two things.
It all starts with equivalents ("how much substance reacts with 1 gram of hydrogen"), so the path to the conclusion can be a bit bumpy. Historically what defined the Avogadro's number was the ratio of masses - mass of a mole of a substance to mass of the single molecule/atom. When you take a different substance, mass of a mole changes, but so does the mass of a single molecule/atom, and the ratio remains constant.
Later it turned out it is more convenient to use Avogadro's number to define a mole, so the definition has changed and whole system looks a bit circular.
If aliens had a planet like ours and were studying chemistry, would a mole be considered 6.022 x 10^23?
No. It is quite possible they would use similar system in which amount of substance is based on the number of atoms/molecules, but choice of the mass unit is completely arbitrary. Remember, "1 g of hydrogen" is where it started, and original definition of "1 g" was based on the Earth size and selection of water as a reference substance. While I can imagine aliens choosing water for a reference, chances that their planet has exactly the same size as Earth are slim.