11” Mid 2012 MacBook Air Display issue
This is not a perfect answer to all your questions but it might help you whatsoever.


Are they right?

From what I can tell, this actually looks like a hardware problem. However, without opening the MacBook it is very unlikely to find the actual cause. You should still try the different startup modes. D for hardware diagnose, opt cmd p r for NVRAM/PRAM reset.


Is there a fix?

This really depends on what's broken. It could be a defective GPU, but it could also just be a broken connector cable.

iMacs from that decade are known to have GPU overheating issues (my Dad experienced this as well).

To analyze this further you would have to take the computer apart and/or take it into a repair shop. If you think you can detect hardware problems yourself, I suggest following this iFixit guide and open the MacBook yourself. For example, a broken cable could be detected by basically anyone, motherboard repairs are obviously for Pros, but in general possible.

The last two questions are so close, I am going to answer them as one:

Worth it to repair/get a new one?

This very much depends on how much the repair would cost and how happy your wife is with this machine.
But as a general advice I would actually look into buying a new MacBook, since 8 years for laptop is not a bad age, especially for a low-speced MacBook Air 11&quot;. Even the cheapest new MacBook Air from this fall will feel lightyears faster and actually seems to be a pretty good package as early reviews indicate. However, if you want to get one of those shiny new M1 powered Macs, keep in mind that these are the first ARM processor Macs, so you might run into software compatibility issues, so always check that first!

More info about these new Macs: MBP, MBA or MacMini?; Another Review, A WIRED Review, why you might not want to buys these new Macs