I've snuck into Ramirez' cellar and stolen the purse from his belt. Garret says "It may be..." but is then cut off by the misson ending! I've checked some FAQs and I'm supposed to be sneaking out of the house with the guards alerted instead.

I'm then sent to this mission called "Guild" that there doesn't seem to be a video briefing for (I can't see the videos in-game so I'm watching them on the desktop using VLC). I don't have a clue what's going on. Has anyone had this happen to them?

The briefing video for Guild is number 15 it turns out. The mission was new in Thief Gold.

Can't remember, but I think this depends on difficulty. If you're playing on normal, some missions just end once you have all of the objectives done. On harder difficulties you need to get back to safety. For example, in Down in the Bonehoard, on normal, you need to just get the Horn of Quintus and the level ends; in harder difficulties, you need to actually go out.

And the reason most walkthroughs mention this is that most people just assume that the normal difficulty is not quite challenging enough and they think most people want to play on hard. Got to say, I didn't, at first. But now I'm replaying it on hard. =)

As for videos not working, there's threads about how to troubleshoot them. (I'm on Win7 and I need to run the games as admin for the video playback to work, for example.)

Expert is the only way to play this game. The new objectives and tweaks are pretty great.