Are the profits of the Islamic Transactions Branch of Banque Misr considered usury (riba) because it is affiliated with a conventional, non-Islamic bank, and what should be done with previous profits if it is confirmed that they were usury?

The ruling on dealing with a bank branch depends on the nature of its transactions. If they are in accordance with the Sharia (definition), then the profit derived from them is permissible (halal (definition)). However, if they are interest-based (riba) or prohibited, then the profit is ill-gotten and must be disposed of by spending it on the general welfare of Muslims and the poor.