Booking a RTW ticket using Star Alliance

There simply aren't any direct flights from Colombo to Mauritius. Checking Skyscanner and Hipmunk, they all seem to go via Mumbai, Kuala Lumpur or Dubai.

Also, somewhere in the booking process you are asked for your 'country of residence' and I suspect this may be a stumbling block to your getting the Egyptian price for your trip, but I don't know if it is possible to overcome this.

I'm a little puzzled by 'Auckland - Fiji - Christchurch' - or is that a typo?

Probably because there are no direct flights from Cook Islands to Fiji.

OP, to reduce the number of stops on your RTW ticket, you could go direct from the Cook Islands to Auckland, and simply buy a separate return ticket from Auckland to Fiji. Also, go to Mumbai instead of Colombo, and buy a separate Mumbai-Colombo return ticket. Don't know if that would work out cheaper, but it's worth looking at. You still have many more evenings on the computer yet :-)

How much are you paying for the flights? Miles or cash? If cash, how many miles total will you gather after this trip, and on what airline will you put it? Personally I would never book a trip like this in advance. I think it's insane.

Is your whole trip flights back-to-back? No overland segments? No budget flights? More insanity (in my opinion).

I don't see anything good between Colombo or Mauritius either, which is a reason I don't like alliance RTWs. Consider just flying that segment on your own, or changing your trip up. Itasoftware is a great tool to search for flights within a specific alliance.

My understanding is that you don't have to be a resident in order to start in a cheaper country, but how much do you save by starting in Cairo, vs how much do you pay to get to/from Cairo?

have come undone when trying to find a flight between Colombo - Mauritius, It seems it should be possible but it displays no flights for that connection which seems a little odd.

There aren't direct flights from Colombo to Mauritius (neither with airlines members of Star Alliance nor with other airlines). In order to go from Colombo to Mauritius with airlines members of Star alliance, you have to make Colombo-Bangkok-Johannesburg-Mauritius or Colombo-Singapore-Johannesburg-Mauritius or Colombo-Istambul-Johannesburg-Mauritius or even more changes of planes... In other words, nightmare routes that imply big detours... not so odd you aren't getting results for that leg.

Solo travel is absolutely best. many reasons.

In your case manditory.

I highly advise against assuming you'll get mileage points just because you fly each leg with a star alliance airline. I've had to fight for mileage and this last trip which was Asia to N. America, my repeated requests for the mileage have gone ignored. It's just a scam to get you to spend money with them.