When you moved some of your apps to the microSD card, that means for those 'moved' apps parts of them were indeed moved to the card, but it's not a matter of the entire app gets moved, some parts of each of those apps remain on your phone's internal storage. So now without that card in its original state, some of your apps might be fully or at least partially 'broken'. You can hopefully fix that situation by going to the Play Store and just reinstalling those originally moved apps. And from now on, if you're going to do something with that microSD card, move the apps back to your phone's storage before pulling it out and re-purposing it.
As for chkdisk even though your card was formatted as FAT (or FAT32 or xFAT) it can only fix FAT and/or Windows related problems (if chkdisk can even do that thoroughly but that's a different argument). Things relative to Android and its different file system and different file hierarchy are outside chkdisk's capabilities.
When it's a matter of storing just files on your microSD card, the card itself is just storage media. Whether the card is in your phone or sitting on a table, your phone is still fine as is. But once you moved some apps to it, then the card became a de facto part of your phone and how it works. Because some apps require that card to be there, once you pull it out and alter its original state, that creates a problem. Windows doesn't use the same file permissions or file hierarchy so it's one thing to just use a card to transfer files and another when there a different operating systems involved.
