[Sundraoi]

First, are similar factions in different cities independent? For example, there's several temples of Kossuth and Cyric floating around, is each temple it's own unique faction? Where a player is limited to joining as a member of one temple per city? Or is someone who joins the temple of Kossuth in Bezantur also a member of the temple of Kossuth in Tyraturos?

Yes. ALL temples and guilds are separate from their similar faction in a different city. This includes the thieves guilds and assassins guilds found in other cities.
The only faction that may operate out of multiple cites are the legions. They operate out of their tharch which may have more than one city/town within it's borders. In those cases, they have access to legion barracks in all cities/towns of their tharch.

Second, are there options for expanding an existing faction? For example, let's imagine that Alek Kelter decided to toss out everything about his character, suddenly become a serial killer, and manage to become an officer in the Tower of Swift Death. Could he then go on to say "Hey, we should expand our reach" and found a chapter of the guild in Moszabbar?

Well, unless he's a priest of Bhaal (possibly Cyric by now?) he won't make it to the higher ranks within that guild as it's a temple. I get your point though. Yes, you can work on expanding their reach. To do that it would work the same as creating your own player owned faction which you can read about in this thread.