Short answer

To make that a shared file or folder appear in "My Drive" of the account to which those items were shared, the account user should move those items to the account "My Drive". Otherwise the items will become orphaned.

Proposed "scenario"

1. User A created a folder.
2. User A shared the folder with User B and made User B owner.
3. User B logged in and can't find the folder in "My Drive".
4. User B logged in and look for the shared folder in "Shared with me".
5. User B move the shared folder to "My Unit".
6. User A transfer the ownership of the folder to User B.

Explanation

From “Shared with me” - Drive Help

The "Shared with me" view in the left-hand side navigation lets you see the files and folders that other people have shared with you, beginning with the most recent.

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Add files to “My Drive”

To make sure you have the most current version of a file in the Drive folder on your Mac or PC, you need to store it in “My Drive” in Google Drive online.

Here’s how to add something to “My Drive” from “Shared with me” in the new Google Drive:

1. Sign in to drive.google.com.
2. Click Shared with me in the left-hand side navigation.
3. Hover over a file and click the Add to My Drive icon. The files you chose will automatically sync to the Google Drive folder on your computer.

From Find your files - Docs editors Help

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If an item in Google Drive loses all of its parent folders, it becomes an orphan. The item still exists, but it may be a little harder to find.

How does a file become orphaned?

Files are orphaned due to situations related to sharing and permissions. For example:

1. User A creates folder X in his Drive.
2. User A shares folder X with user B.
3. User B creates item Y inside folder X.
4. User A trashes folder X, and empties his trash.

At this point, item Y becomes orphaned. It was never created inside of user B's My Drive, and its parent folder (folder X) is now gone. Note that item Y is not deleted along with with folder X because user A can't delete user B's file.

To prevent that a file that it's ownership will be transferred become an orphan file, do the following:

1. User A share the file with User B. Repeat as necessary.
2. User B add the shared files to "My Unit" or any folder beneath it.
3. User A transfer the ownership of the files to User B.

I don't think you can check multiple documents at once, but to find statistics for a single Google Doc try Tools -> Word count or Ctrl+Shift+C

Via Google Support: "Count the words in a document"