Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Many Fatawa have been issued regarding your first question. The conclusion is that jewelry worn by women is not liable for Zakah according to the opinion of the majority of the people of knowledge.
However, if this jewelry is worn only on some occasions, then please refer to fatwa:82873.
But if this gold is saved or accumulated for sale then it is liable for Zakah.
As regards your second question, the wealth which is left by the first husband will be divided as follows:
The wife will get one eighth (1/8) portion of the inheritance, and the rest will be divided amongst the children.
Allah says: "But if you leave a child, they get an eighth of that which you leave after payment of legacies that you may have bequeathed or debts."
Allah also says: "Allah commands you as regards your children's (inheritance): to the male, a portion equal to that of two females."
With regard to what this woman has left, whether it was what she had inherited from her first husband or other wealth that she had possessed, it will be divided as follows: Her husband gets one fourth (1/4) of the inheritance, Allah says: " But if they leave a child, you get a fourth of that which they leave after payment of legacies that they may have bequeathed or debts."
And the rest of the wealth will be divided amongst all her children from her first husband and second husband, the male will get two portions of that of a female.
We draw your attention to the fact that in the matter of inheritance, you should not rely only on one fatwa, rather you should take the matter to Islamic courts or one of the people of knowledge to grasp all the knowledge about who will inherit and who will not, and all relevant matters that could be forgotten or neglected by the questioner and which might not have been mentioned in the question.
Allah knows best.