Are the profits from money deposited in a non-Islamic bank lawful (halal) or unlawful (haram), and if they are unlawful, is the solution to transfer them to an Islamic bank, and what are the Sharia-compliant evidences for that?

Allah has forbidden usury and has warned those who consume it with war. Non-Islamic banks deal with forbidden usury, therefore, deposits must be transferred to an Islamic entity that does not deal with usury. As for the forbidden usurious interests, they must be disposed of by spending them on the poor, the needy, and public welfare.