Okay, honestly, our issue is his entire powerset.

An aura of deathlessness basically destroys any fights within that radius, be they player vs player or player vs NPC. Especially given that Dolls, Puppeteers, and Marionettes can regenerate. I also feel that it is frankly overpowered, preventing so many things from dying with no way to prevent it at all.

The second one's problems have already been explained.

Finally, all physical influence(and indeed, all influence whatsoever) of a Puppeteer on a Marionette vanishes when it is removed from its host. With the exception of a very, very specific kind of power(Rain's example, where it's a blood infection and technically qualifies as never leaving the Marionettes), the Marionette is totally returned to normal.