I'd like a good answer to the first question as well (it would be ideal if there was an easy way we could host it ourselves), at least OpenWhisperSystems does not belong to Twitter [0]:
> Whisper Systems was a company focused on the development of mobile security software, which was acquired by Twitter in late 2011. Twitter very generously made some of the Whisper Systems software available under an Open Source license (GPLv3), which has since been under open development by the community. The software has seen a number of new releases based on that open development, and we’ve been calling the project for this continued work “Open Whisper Systems.” Welcome to the project’s new home.
> Whisper Systems was a company focused on the development of mobile security software, which was acquired by Twitter in late 2011. Twitter very generously made some of the Whisper Systems software available under an Open Source license (GPLv3), which has since been under open development by the community. The software has seen a number of new releases based on that open development, and we’ve been calling the project for this continued work “Open Whisper Systems.” Welcome to the project’s new home.
https://whispersystems.org/blog/welcome/