In all honesty that stone is more metaphoric than a possibility to make. Alchemy is just basic chemistry using the elements for example taking dirt and water to make mud. Or air and water to make a cloud. Granted there's more to it but you get the general idea. However the basic idea of it is to learn how everything is made from astral to physical and the strong connection between the two. However the stone reference and turning lead into gold goes into " spiritual alchemy " which pertains to the soul and the many different aspects of that. But as far as a physical thing and can you make it in your basement no. Even astrally it can't be done unless you get the metaphorical meaning behind it.
The stone is a complex working of magic, science and minerals. It is said that only a pinch of its dust could turn liquid lead to gold and all other metals to gold. However the only one ever made was destroyed due to its pagen roots. No one knows the exact recapie but we believe it was as if the stone was alive with power. Unfortunately since none knows how to make one we can only attempt though most attempts are catastrophic failures resulting in explosions.
Huh, not trying to sound sterotypic but, it sounds like it needs (a) human sacrafice. If it's living it'll need a soul(s). Since it is powerful life is the one thing to make it perfect. It is just a theory though.