Nostromo Public folder - so basically anything placed in this folder/subfolders will be publicly viewable without logging in.
First of all, there will soon be a new multi-user login system, which also allows non-login user (public view).
As for having a specific "public" folder, this can be managed by how you setup the logins. Each user can have their own "root", and each user can have different write permissions (for uploading etc). There won't be different logins PER FOLDER, because Files Gallery doesn't control your folders.
Nostromo Sync - some sort of script that would run on PC/MAC that would automatically sync the contents of selected local folders with online
You mean Files Gallery connects to your server by FTP, downloads all files to local? This is a bit outside the scope of Files Gallery. Even if this is possible in PHP via FTP, it would need to be a separate operation, because it can't be done at the same time as running Files Gallery in browser ... The operation is too slow, and would need to be a separate script. And if it's separate, you could use RSYNC or an app like allwaysync.com.