If you are stopping for greater than 24 hours in London and Casablanca, then you cannot spend more than 24 hours in Madrid as it would be a third stopover in your continent of origin.

You do not have to return to Cairo although there is a possibility that BA will audit your ticket and demand payment for all the separate segments. This is a possibility but not a probability. Others have skipped the last segment on a RTW without any problems.

I do not think you will be able to apply for a Russian visa in one country and pick it up in another. Why not just apply in South Korea before you leave?

I'm traveling and do not have the BA CAI information with me. However, you should be able to find it easily here using the search function. Try searching "Sobhi" as that is the name of the lady in CAI who handles the RTW tickets. They do not publish an Email address so you will have to call them and FAX them your information.