1. If you move a parent task, the child task should follow as well. However, this behaviour is only available in the web app, desktop app and any of mail client plug-in. So if you're using an iOS device for example, it would not work.
2. You can use ":to others:" (don't include the quotes) to search for tasks assigned to others.
我想查看特定共享人的任务，如何做？例如 ":to username1:"
Unfortunately, that is not possible as of the moment.
Task in shared projects should still be backed up and available for you restore.
We don’t normally give out ETA on when features are released. I suggest to create a request in the Votebox https://todoist.com/Vote/ for the meantime.