Can I re-use beurre blanc the following day? And how do I reheat it?

good luck. Sometimes it will be re-usable, but most of the time it will separate. Re-heat it slowly over really low heat. If possible, use a double boiler. You may also want to add a touch of heavy cream. It will help it hold together.

Your success will depend on how you made the sauce to begin with. If you made it the classic way, you will have a harder time re-heating it.