Is depositing money in "United Egyptian Bank" with the available variable-yield certificates considered an Islamic transaction compliant with Islamic Sharia, and are the resulting profits free from the suspicion of usury (riba)?

If the Islamic branch of the bank is independent of the interest-based branch, then there is no objection to depositing money in it. It is not a condition to know its activities as long as its Sharia supervision is not lenient in violating the Sharia. It is not possible to rule on a specific bank without knowing its activities and its Sharia supervision.