To make the scabbard fit snugly, glue in a thin piece of soft wood (pear, for example, no beech, oak or redwood) to one side of the scabbard´s mouthpiece. Don´t worry if the fit seems too tight at first, the grain will be compressed in due time.

Olive oil and fine pumice powder work well against rust if the spots are not too big. Olive oil contains acid that attacks oxidation faster than it does metal. Daub with olive oil, then "salt" with pumice. Then polish with a lint-free cloth. Repeat as necessary.

For larger or deeply rusted spots, first use copper mesh to remove the worst parts.

It may have been that the rusting occurred during transport, when the blade was subject to rapid temperature / humidity changes. The scabbard creates a kind of separate microclimate. A fine (!) coating of ballistic oil helps if you are going to store the sword in the scabbard while travelling, but is a bugger to get rid of when you´re backstage (kind of like checking the oil on your car while in costume).

Hope this helps!