How can a new company be established with a foreign partner according to Islamic Sharia, specifying the shares of the partners and the profit distribution, and is it permissible to set a salary or a percentage of the profits in return for management?

Partnership between you two is permissible on the basis of Mudarabah (profit-sharing) or Musharakah (joint venture). The amount of capital contributed by each partner and their share of the profits must be clearly specified therein. It is permissible to give the working partner a larger share of the profits than his capital contribution in exchange for his work. However, it is not permissible to give a partner a fixed salary as part of the partnership contract, unless it is for work that is not required of him by the partnership contract, in which case a separate contract for that work would be permissible.