I can only tell you what I have experienced. Mine tends to slow down it's growing habit in the winter and loses some leaves. I bring it inside during our short winter 3 months and it mainly stays outside in the bright shade for the rest of the year. In the winter, I *might* be lucky to get one new leaf in 3 months. It sits in a south-facing window getting as much winter sun as I can give it.
Your plant seems to be replanted a little deep. But it seems healthy. The "ginger root" you describe seems like it might be what's left of part of the plant that has deceased, perhaps the Mother plant from where the others that surround it came from. Peace Lily's do not a like a lot of water. It likes well-draining soil and even moisture. It does well in shade but really loves some bright light. Keep us posted.
