How to remove glue then re-glue two pieces of china together?

I inherited a cake plate that has a pedestal. The two pieces had been factory glued together. Somehow the two parts dislodged. Now that they're separate I see a rock solid flat glue piece the size of a half-dollar on the top of the pedestal.

How do I remove that old glue without breaking the pedestal?

How do I then adhere the two pieces of the cake plate together?

The manufacturer of the plate is unclear and it seems to be nothing of value. The only words on the underside of the pedestal are "Victorian Garden From the Private Collection of Georges Briard (?)"