If you're walking around in Alexandria and some guards attack you for no reason while other guards don't - are there different guards from different factions? Do the guards all serve Ptolemy the pharaoh or not? Who are the blues and the greens and do they have guards too?

If you kill a bunch of people from a certain faction do they become hostile to you?

I've killed dozens of men and I don't know who they were.

I've never been attacked by guards just walking around, only if I had started shit or was in the middle of a side quest where they were hostile. I have found that if you ever join in a fight when guards are fighting bandits or whatever then the guards will be hostile to you regardless of who you attack first in that scenario though, which can get hectic.

Alexandria would be all Ptolemy though, and the Blues and Greens are the names of Chariot.. I guess teams for lack of a better word?

I wouldn't think about it too hard. There aren't really any "allied" or "enemy" factions and there are no consequences to murdering a bunch of guards.

Having said that, up until late game you generally aren't attacked on sight unless you enter a restricted area, so if your compass is glowing red, guards will attack on sight.

Aren't there like 3 factions? (Greeks, Egyptians and Romans) + bandits? Haven't thought about it honestly.

I think mechanically there is really just Guard and Bandit.

Like Bayek is ostensibly 'allied' with Cleopatra and her faction but guards in those areas will still stab you in the face if you attempt to roam around restricted areas or cause trouble.

they are part of an order of guards formed in the times of antiquity when the ancient aliens enslaved the men of earth to build big curvy towers and hexagon puzzle rooms