If you know what chemical group an element is in, what can you predict about its electron arrangement?

it's atomic number reveals it's amount of electrons, each shell have a certain amount it could carry it's

2-8-8-18-18-32-32

It's called the octet rule.

alchemy hadn't scientific methods of study, appeal to mysticism and fantasy, the knowledge of chemistry and physics were modest at that time.

alchemy was - but as new rules were discovered it either changed into chemistry or it became "unscientific".