Is zakat obligatory on shares purchased for trading purposes that are held for two or three months? And do companies pay zakat on their shares? And is zakat obligatory on gold designated for adornment if most of it is not worn?

The zakat on shares has a detailed methodology. As for the wife's jewelry prepared for personal use, the majority of scholars hold that zakat is not obligatory on it, and this is the preponderant opinion. However, giving zakat on it is good, as it is desirable to do so to avoid scholarly disagreement.