The large-scale solar power option is to convert dilute solar power into concentrated heat energy then convert that into electricity to export to the populated parts of the country.
Some estimate that the US could meet 90% of electricity demand by tapping into the solar energy in the Southwest.
Question #1: what would the regional environmental impact be?
Such a process would take tens to hundreds of gigawatts of heat out of area, potentially altering regional weather patterns.
my guess: irrelevant. each project would be permitted individually. each would only have to prove that their incremental impact would be negligible, which they would be.
Question #2, #3, #4: if Africa weren't such a mess, how much energy could be exported from the Sahara region to Europe (where energy costs are flat out ludicrously high - $.30/kwh is not unusual)? How would that compare to the oil energy exports from the Middle East? Would the income from so much power be enough to give Europe the economic incentive to finally clean up the mess they made in Africa during their empire-building days?
my guesses: more than they could use, 5-10x more, i have no idea
Question #4: (and this is the most appealing one for me) is there an appropriate technology low tech, local material-based way to convert sunlight into electricity for the hot, sunny, and arid regions of the world?
Arid is the tough part. Water is the most common working fluid. Maybe if you did it closed cycle and assumed that dirty water was available and clean water was a desirable output you could come up with something that made a bit of electricity and a bunch of purified water.