nikki,
Thank you for the question. To see if it is Porcelain , hold it up to bright light. Wave your hand back and forth between the light and the vase. If you can see the shadow of your hand
moving across then its porcelain.
Then very carefully , extra hands/eyes would be good at this point, put the two halves together.By feel and eye determine if the parts match exactly. If they
do it should feel rite. Its called “lock in’. If they “lock in” perfectly , you can use a clear glue that cures in sunlight. Let me know about the above questions. As an alternate source , you can look up the topic “Light Curing glue” under my name in the archives at Antiquerestorers.com. You can also look me up on an Google search by combining my name , Peter Dale , with the words “light curing glue ” and it may take you to other archived forums.PS if the halves do not line up perfectly then chances are the vase broke across a fired stress line and it will never go together correctly as the vase did not want to join that way , Thats why some porcelain items like cups , crack with across a built in stress line
with a very slight rapp.