Is it permissible to deposit money in an Islamic bank with a variable profit rate? And how is the money received monthly from the bank to be zakated?

Fluctuations in the profits of Islamic banks, whether rising or falling, are natural because they are investment profits that are not guaranteed. The profit may decrease, increase, or cease to exist, but a common profit-sharing ratio must be agreed upon. As for the zakat on funds deposited in banks, zakat is obligatory on what has completed a full year (hawl), and it is not obligatory on what was consumed before that.