Is any part of alchemy possible?

Yes! First alchemy was NOT all about trying to turn things into gold. That just shows the lack of information on the subject. True alchemy, historical alchemy, was about creating substances that were better than their base version. Example: Back in the day you would take say mint tea for a stomachache. Mint tea is good, but an alchemist would make the herb into an elixir that would work 10x better and faster. Alchemists are the ones responsible for creating gunpowder and introducing explosives to the world. They are responsible for developing many of the processes we still use today in chemistry and pharmacy. They have also discovered new elements and methods for producing pure metals.

Everyone that doesn't study or understand or research alchemy only thinks its about trying to turn lead into gold or some other equally preposterous thing (except through very specific scientific methods). Alchemy was about studying the natural world, creating medicines, and finding new things and methods to help people.

Sort of. It laid the foundations for the experiments that eventually led to chemistry (even though almost all of it was wrong).

The problem is that, at the time, atoms and molecules hadn't been discovered yet. Without that knowledge, transmutation isn't that far-fetched an idea... after all, if two compounds can be transmuted (i.e. a chemical reaction), then why couldn't lead be turned into gold? Now we know that it's because gold is an element, and is immutable (as far as chemical reactions are concerned).

Elements can be transmuted, though it's more "particle physics" than "alchemy". Whereas alchemists tried to chemically transmute elements, physicists can transmute them by bombarding them with high-energy particles. They can stick together and form an element higher up on the periodic table, or a particle can blast another atom apart, forming two elements lower on the table. It can even happen naturally - a substance is exposed to the right type and amount of radiation can absorb the radioactive particles and increase it's atomic number (or it can absorb a neutron and become a different isotope). Likewise, radioactive materials are radioactive because they spit out particles, becoming elements lower on the table (uranium decays into lead, for example).

"Alchemy" lead to "Chemistry"

Algebra was an an advanced form of arithmetic

Alcohol was a refined form of wine and beer

Arabs like to use "Al" in words