Are all family members' salaries counted along with the profits of the commercial store to calculate Zakat, and is Zakat al-Fitr distributed in the same way?

Zakat is not obligatory on anyone unless what they own reaches the nisab and a hawl (full lunar year) has passed on it. If each partner's share in the commercial shop has reached the nisab by itself, or by combining it with other similar assets, and a hawl has passed on it, then zakat is obligatory on them; otherwise, it is not. As for Zakat al-Fitr, it is obligatory on whoever possesses more than their and their dependents' sustenance for the day and night of Eid, and more than their dwelling and a servant if needed.