Can a Puppet Master see and/or control items on Puppets?

Basically, how do items and puppets interact with each other:

1. Does the Puppet Master receive items given to puppets?
2. Can the Puppet Master use items held by puppets during the night?
3. If a Puppet is holding an item and that item is stolen during the night, will the Puppet Master receive a notification telling them that they were robbed?

And maybe more, if you can think of any other interactions when writing an answer to this question.

Bonus question:

4. What happens if a Puppet is holding the Heart of Fenrir when the last wolf dies?

From my current understanding (had a talk with Kirschstein about this), I have the following answers to some of these questions.

1: The PM receives all items given to Puppets or themselves 2: The PM can use all items held by one of its three (living) avatars

The PM doesn't know which item is held by which avatar.

3: I have no clue. Makes me wonder if the notification targets the 'avatar' or the 'holder of the item'...

4: No clue as well!