Dr-Rufus, you got some bad advice! Red oak contains tannin that reacts in the form of oxidation when exposed to water, alcohol, iron, sunlight. Vinegar is often used along with old iron nails to make a black stain. These all result in deep black stains penetrating into the grain, particularly summer growth, as you can see.
Lots of finishes are called tung oil, some are, some aren't. Either way, they are pretty terrible at protecting an open grained species, like red oak, from all of the above.
Since those are rather simple to make, toss those and use a finish that will stand up to kitchen use, alcohol, detergents, hot water, abrasion. You will need to build a fairly substantial film of the finish you choose. I use Man-O-War spar varnish for kitchen wood that get's abused. 5 or 6 coats.
Mold is killed by chlorine bleach. Just placing a drop on an inconspicuous area will tell you if it's mold, it will start to disappear.