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Yep, sorta hard to hone with oil on the blade.

I have blades like that,ren-wax them before honing and use distilled water,works.

Not rust but Strap burns are common:)

Have kept mine in leather rolls for yrs with never an issue.
Do not think it is a moisture issue with leather,People have expressed concerns about acids and tannins from the tanning process.
But...