No Skills appear

Is Felicity doing the No Skills, No Problem challenge?

Your third picture has an event tracker at the top left corner. I can't see all of it, but what I can see is that the event's title ends with the word Problem. This, along with the description of the trouble you're having, makes me think that you do have No Skills, No Problem as an active challenge scenario for that save. Here's the description of No Skills, No Problem from the game itself:

A sim cannot seem to get skillful at... well, anything! It's made everything more difficult, from relationships to holding a steady job, and, as a result, they've had to figure out ways to work harder or smarter than everyone else. Can this unskilled Sim figure out how to hack life and earn some sweet Simoleons?

The actual effect of the challenge is to prevent the affected Sim from gaining any skills, just as you described. The solution is to either complete the challenge, by having 400,000 Simoleons, or cancel the challenge by clicking the trashcan button at the bottom of its event tracker.

Yes, that appears to be the case.

I never tried adding other Sims to the household during this challenge before, but I have now. The original Sim, who started the challenge, still can't learn any skills but the two Sims I had her move in, just for testing purposes, are both learning skills. One, an adult, has learned Charisma and Parenting. The other, a Child, has learned Creativity.

No Skills, No Problem is probably my favorite challenge scenario. It's fun finding ways to earn money without using skills. My current Sim took a job as a Scientist. The Scientist career is based on breakthroughs, rather than skills, so it's one of the few careers where promotions are still possible. It also has a lot of cool gadgets with money-making potential.