Is Zakat obligatory on gold that does not reach the Nisab if it is not added to other money not owned by the gold's owner? And is she sinful for not knowing the obligation to add gold that has not reached the Nisab to money to complete the Nisab?

Gold designated for adornment is not subject to zakat, even if unused. This is the view of the majority of scholars. It is not necessary to combine jewelry with cash to complete the zakat nisab. Even if it were held that zakat is obligatory on adornment jewelry intended for use, only cash upon which a hawl (full lunar year) has passed would be combined with it. The mentioned bonus has not yet completed its hawl, therefore it is not to be combined according to either opinion.