I partially misunderstood, my point was just that you can do it without flaps with very little practice, but I get it. As for why it says your flaps are fixed but it’s not letting you put them down, my main theory is this: Flaps in the Cessna 172 are operated by electricity. There’s a motor in the right wing. One of the items that can become damaged is just “Electrical system” and if that is sufficiently damaged, I could see it preventing the flaps from working even if other electrical components are working. In your original screenshots, Electrical system was marked as out of order. Unless you already fixed that, that would be the next thing I recommend repairing.
But as far as the issue goes, unless your original crash was caused by a bug, there isn’t a problem here, really. You take on a ton of risk when buying an aircraft in career mode. But you’re not prevented from continuing your career, you can keep doing the same missions you were doing before you bought the plane. It’s frustrating, but I kind of like that. And I say this as someone who just reset my own career due to losing my plane to a bug (skipped taxi and the plane was instantly destroyed.)
Closing thought, here’s a video of a no-flaps landing I did in the 172 last night:
This mission put me on a long final, the video starts when I’m rougly 4.5nm away from the airport, so I had plenty of time to slow down but you can ignore the blue boxes in missions and get as much distance as you need. I intentionally get some speed (around 110 kts) to show how much I’m able to slow down without flaps. Even with power, I slow to 102kts just by having my nose up. At 34 seconds, I cut my power and drop to 74 knots in around 15 seconds. I actually have to apply quite a bit of power afterwards to not continue sinking. At around 2:00 I’m coming into the airport intentionally high, meaning I’ll gain speed if I nose down, so I do a slip at 2:21 (right rudder, left aileron) which slows me from 70 kts to 60 kts in just a few seconds. After leveling out, I do gain back some speed but still land well within normal landing speed range. I’m not trying to beat a dead horse here, but you said a couple times that slips “don’t work” or that it’s “impossible” and I’m just encouraging you to give it a try if it lets you continue to use your 172 in career.