I think it is better to think of geass users and masters in terms of levels (well, since that is what they are). One starts out as a geass user after making a contact, then eventually kills their master and gains immortality at the cost of their geass, but this does not necessarily mean that the rank of power they gained while leveling up their geass becomes void. So technically, they moved up, so if rank determines whether a user can kill a master, a master will definitely be able to kill another master. Charles already killed V.V., so it only makes sense that he is still able to kill C.C. as well.

About Lelouch's eyes not showing the geass, he probably had his contacts on.

About the mysteries in the series, those are very very minor compared to what has been revealed this episode. They are not central to the plot, and as such I think they will be addressed very briefly.

I doubt your theory is right. Killing seems to be the only way of succession, and C.C.'s original wish was indeed to die (don't forget C.C.'s flashback that proves this point). But that does not have to stay that way, since she just chose to save Lelouch over fulfilling her wish this episode.

About the children in the geass base, please do not forget that the place is a research facility for geass. They are trying to produce them artificially, so they probably did not have a master, or V.V. sired them, since one master can have several million contracts for all we know (two contracts at one time is confirmed though).