Skillet rust (?) and next steps with regard to seasoning
The marks look like bare iron, as though the seasoning has actually been fully removed there. How hard did you scrub?

I use vegetable oil and use only about a teaspoon for the inside cooking surface and sides. Another teaspoon for the outside and underside and handle. You really don't want too much oil or it will become sticky because it hasn't broken down fully, which is probably what happened with your first attempt. I imagine your skillet was already pre-seasoned anyway.

To fix it, heat the pan on the cooker for a bit, then reapply the oil in a thin layer with a piece of kitchen towel, and use another clean kitchen towel to wipe away any excess. The pan should be hot but not searing, the heat apparently helps open the pores of the metal. The surface shouldn't look wet or have wet spots. It should have a sheen to it.

Put it in the oven, upside down, on the maximum temperate (around 240c or 450f) for an hour or longer. When you pull it out, it should be seasoned nicely. The surface won't have a sheen anymore, and it shouldn't be sticky to the touch once it's cool.

You can repeat the process a few times if you think it needs it.