That's not a problem caused by Let's Encrypt, as the intermediate certificate could have changed any time due to a major incident. It's bad practice to hardcode an intermediate certificate.
That's not possible.
That's bad design on the app designers part.
As stated in the thread in the API announcement section:
This change should be a non-event for you and your site's users.
Emphesis on "should be".
If you have adhered to the Let's Encrypt recommendation of renewing 30 days before the end of the lifetime of the certificate, you should be able to put back the previous certificate and you'll have 30 days to fix your app until the certificate expires.