Is money deposited in banks considered doubtful due to interest, and is it permissible to give its zakat to hospitals and orphanages via bank transfer, or must it be handed over in person?

Depositing money in usurious banks and taking usurious interest are major sins. Paying zakat from this money does not absolve its owner of the sin.

It is not permissible to use zakat funds for building a hospital or an orphanage, because the categories for zakat expenditure are restricted to the eight mentioned in His Almighty's saying: ﴿Indeed, zakat expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the traveler.﴾ [At-Tawbah/60].

However, if the purpose of depositing it in an orphanage is to spend it on poor orphans, then that is permissible.

It is preferable for the zakat payer to distribute their zakat themselves to ensure it reaches those who are eligible.