Is it permissible to lease a private car to someone who operates it as an "Uber" taxi, and is this considered a form of prohibited daman/tadmin (guarantee/indemnification)?

Giving a car to someone for their use in exchange for a specified amount of money is a lease contract (ijarah). Jurists define ijarah as: "A contract of exchange, for the transfer of usufruct (manfa'ah) for a consideration ( عوض - 'awad)." The specified rent is a condition for the validity of the ijarah, and this has no relation to mudaraba (profit-sharing partnership) where profit is determined by a percentage, not a fixed amount.