Did the Corinthians respond to Paul's first letter?
Yes, they did. Paul’s first letter did not fall on deaf ears. By the time of 2 Corinthians, Paul indicates many things were corrected. Enough time had elapsed for them to clean up their act and deal with the problems, and evidently they had done so.
Les explains that the Corinthians evidently sent the apostle a letter with a long list of questions about how they were handling various problems, and he dealt with that in the first letter. Then, when we get to 2 Corinthians, Paul seemingly gives the idea that a lot of these things are now corrected. So his first letter did not fall on deaf ears. Les points out that the second letter was probably written months, less than a year, after the first, so enough time had elapsed for them to clean up their act and deal with some things, which evidently they had done. Nevertheless, the first part of 2 Corinthians, up to verse 10 of chapter 6, Paul is more or less defending his apostleship.