Is taking a loan through renting a car whose price exceeds its real value, while the documents remain in the name of the first owner, considered usury (riba)? And what is the ruling on benefiting from ill-gotten gains to pay off debts or build houses?

The description you provided for the lease-to-own contract is insufficient to rule on it. This type of contract has various forms, some permissible and others forbidden, and its regulations have been clarified in previous fatwas.

As for accepting a gift of illicitly-gained money: it is permissible if its unlawfulness stems from its acquisition, such as usury and the like. However, if it is unlawful in its essence, such as stolen or usurped property, then it is not permissible to accept it. The sin of money that is illicitly-gained through its acquisition falls upon the earner, not upon the one who takes it through a permissible means, unlike that which is unlawful in its essence.