Plastercizer - chemical reaction from rubber/ petroleum base material. You would need to redo every board that is affected. Common with all water base finishes. Most common with white wash finishes. Does not matter which brand you use. Warnings are on the bottle.

First photo, looks like someone went out and shredded some bike tires and the residue got on the floor. Not sure what the second photo is caused from. Looks like a hula hoop, unless, it's a road bike tire.

Thank you! That resolved the mystery of little marks; indeed bike tires. Bikes were standing there for a couple of weeks.
Circle is still a mystery.

When you say re-do boards - will refinishing be enough or will they have to be replaced?

Refinish the individual boards that are affected.

Large circles don't just spontaneously appear on floors. Looks like someone set something on the floor that rusted. I'd try some acetone on a clean rag for the footprints.