Is buying two gold sets for two boys (aged 15 and 12) with the intention of gifting them to their future wives (from the dowry) considered a sin, and is Zakat obligatory on this jewelry? And does a woman's jewelry and ornaments become part of the inheritance after her husband's death?

There is no sin in buying gold and saving it for children; rather, the sin lies in using it. Zakat becomes obligatory on it if it reaches the nisab (85 grams) and one hawl (lunar year) passes over it, so 2.5% of it must be given. A woman's jewelry and possessions do not enter into her deceased husband's inheritance if they were from her own private wealth.