Is Zakat Farj against idle preserved ornament ( gold) belong to a spouse ?

[Beyond Tradition]

Dear Brother Joseph,
Salamun Alaikum . I gone through your significant thread about Zakat and understand there is no fixation on Zakat for Muslim .
My question is I am paying income tax to the government . Is Zakat and Salah Farj for any individuals or any community ?
Since Quran mentioned for Zakah and Salah simultaneously so is it the compulsory for a government to established Zakat and Salah ?
If the Chief of the State Non Muslim ( Disbeliever)  then how a Muslim  ( Believer ) can establish Salah and Zakat ?  If Zakat means Tax on income then will it be okay for a Muslim when Government is not a Muslim  ? Sadaka is different and any Muslim can spend any amount to the specific ground what Quran specified already . But about Zakah there is no mention ( may be )  where  it should be spent .
Is Zakat Farj against idle preserved ornament ( gold) belong to a spouse ? Many Muslim teacher here give a "Fatoa" that Zakah must be paid on idle gold which preserved at home belonging a women . I can not justify this concept in the light of  Quran .   

Please make me clear to follow the instructions from God .