Re: In the No Skills No Problem scenario my Sim is gaining skills, why?

I can see that from your screenshots. I also see the household includes a pet, and I suppose it's possible the challenge got assigned to the pet, instead of the Sim, if they were both created in CAS when you started the scenario. (Stupid, I know, and it's just speculation) The scenario should still finish once your household reaches 400,000 simoleons or you could just cancel it.

Whatever went wrong, I don't think there's any way to fix it, so I would suggest just starting over. It looks like you are still fairly early in the scenario, and you won't get the full experience if your Sim is earning skills.