Is it a condition for wealth, if it reaches the nisab, that it be surplus to the needs of the zakat-payer and those he supports, as well as their housing and clothing for one year, in order for the remainder to be subject to zakat, and does the same apply to zakat on crops and fruits?

Whoever possesses the minimum taxable amount (nisab (definition)) is obligated to pay zakat (definition). The majority of scholars do not stipulate that for zakat to be obligatory, the amount must be surplus to his and his dependents' sustenance for the entire year. However, the Hanafis stipulate that for zakat to be obligatory, the nisab must be surplus to one's essential needs for the entire year.