What exactly happened at the end of the Thieves Guild questline in Oblivion? Did time literally get re-written after the curse was lifted or was the Guildhall and other stuff always there but the curse made it so no one could remember its existence or something? If time had been changed then why can people still remember their lives from when the curse was still in effect?

Also are the different sections of the Thieves Guilds found in separate provinces completely different guilds from each other or do they have some kind of connection that binds them all together other than just stealing things?

I think each branch is different, from what I've seen the TG in Morrowind is way different then the one in Cyrodiil and the one in skyrim during the 4th era is more of a group of thugs then thieves as mentioned several times.