All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Zakah is obligatory on the money that reaches the Nisaab (i.e. the minimum amount liable for Zakat) by itself or with other money added to it and a whole lunar year should have elapsed on possessing it; for more benefit, please refer to Fatwa 93584. Therefore, there is no Zakah on your monthly salary.
As regards the taxes that the government deducts from you, then this does not exempt you from paying Zakah on the gold that you possess. Zakah is different from tax in regard to the categories on which it is spent; for more benefit, please refer to Fatwa 83919.
With regard to the golden jewellery that your wife possesses, if it reaches the Nisaab, the scholars differed in opinion about the obligation of paying Zakah on it. The opinion that we adopt here in Islamweb is that it is not an obligation to pay Zakah on ornaments that are prepared for use (for beautification); for more benefit, please refer to Fatwa 82925.