Title: FAQ ...
Director 3.0 was originally written by primarily Eric Wang (2017) and Omkar Kulkarni (2019). The current version of Director, Director 4.0, was written by John Beutner (2020) and Theo Ouzhinski (2020) based off of Director 3.0.
Short answer: No.
Long answer: An offline mode for Director would be very limited. Since your site runs on a server at TJ, you wouldn't be able to view your site, only edit files (at least for dynamic sites). Additionally, such a system would be very difficult for the Director developers to implement technically, and the slight benefit gained does not outweigh these concerns.
If you really need to work on your site offline, you may want to put your code in Git and upload it to GitHub or GitLab.
On my site's main page, I see a Database Shell link and an Alternate shell link. What's the difference?
Database Shell gives you a shell where you can type SQL queries and see the result. However, it does this by connecting directly to the server, rather than running the mysql or psql commands (which was what previous versions of Director did). As a result, you can only enter normal SQL queries -- commands like SOURCE in MySQL and \dt in PostgreSQL won't work.
Alternate shell runs the appropriate mysql or psql command to connect to your site's database. In this shell, commands like SOURCE in MySQL and \dt in PostgreSQL will work. However, for complicated technical reasons, this shell type takes much longer to load, so you may want to use Database Shell for quick operations.
A previous version of Director allowed for the use of a webhook to automatically update from a Github repository. We have no plans to reintroduce this into Director as explained here.
If you require git, you can install it following the instructions here.