Is it permissible to fulfill a vow from money other than the amount from which the vow was made, or by selling the necklace that was bought with it to fulfill the vow? And is it permissible to give the vowed amount to the mosque for it to distribute to the poor, instead of giving it directly to the poor?

You are not obligated to sell the necklace. Instead, you must donate the vowed amount from any source. If the vowed charity is for the poor, it is not permissible to spend it on others, such as mosques. However, it is permissible to authorize those in charge of the mosque or others to deliver it to the poor.