Maintenance for the week of March 25:
• [COMPLETE] ESO Store and Account System for maintenance – March 28, 9:00AM EDT (13:00 UTC) - 12:00PM EDT (16:00 UTC)
Guilds can be cross faction, however when the guild is created you still need to designate a main faction and while I am not sure entirely what this choice dictates, I do believe that it affects claiming resources in pvp but this is speculation as I haven't tested it. Also, while you can have people from other alliances in your guild it will still not allow to group with them in dungeons or pvp.