What is the ruling on doing good deeds with money obtained through a loan, such as printing Qurans, building mosques, and sponsoring orphans?

If the loan is interest-based (riba), the money acquired from it is not suitable for drawing closer to Allah with. One must dispose of it by spending it on general Muslim welfare, such as building mosques, with the intention of getting rid of the unlawful, not drawing closer to Allah.

However, if the loan is interest-free (a good loan - qard hasan (definition)), then it is permissible to borrow for acts of righteousness, such as sponsoring orphans and distributing Qur'ans, with the caveat that one should not borrow if the borrower does not have the means to repay, due to the gravity of debt.