Yes, BA charges heavy fuel surcharges

With the on-line tool, which airline will ticket your itinerary depends on which you choose for your first flight segment:
- BA if CAI-LHR
- IB if CAI-MAD
- RJ if CAI-AMM (well actually AA does the ticketing for RJ)

Getting AA to do the ticketing means you will only pay AA's fuel surcharges - it doesn't gather the surcharge for other carriers. So in this case how much you pay will depend on how many 'over water' AA segments are in your itinerary (AA has surcharges only on its long-haul 'over water' flights)

Can't help you ticketing through an agent in Cairo - perhaps others can