I'd like to send a DM automatically from Llama. Llama supports Intents, but I can't work out how to send a tweet via an Intent in the background. Is this possible?
It's unlikely that any Twitter app offers a way to do this. In general, intents are used to start an action that requires user interaction to complete, or at the very least ask you for confirmation.
If an app offered a way to send a tweet automatically via an intent, it would also have to require the app sending the intent (Llama in this case) to have a permission created by the app handling the intent (the Twitter app). Otherwise, any app on the phone could send tweets without your knowledge or permission. Llama would have to be written to ask for this permission, and since it isn't, it wouldn't be allowed to send the intent anyway.
Alternatively, it would be possible for the Twitter app to offer such an intent, but ignore the intent unless it was sent by Llama (or better yet, using a configurable list of allowed apps). This is how many apps' Tasker integrations work. Since this is a pretty niche need, I don't know whether you'd be able to find an app that works this way. You might find that there's an app written this way specifically to act as a Llama plugin.