I gave you a direct link to the file in order to make it easier for you, but I obtained that link from the support site for North America.
Go to support.dlink.com, type DIR-615 in the search box, select the model. Select DIR-615_REVC in the right panel, which is what you have (Rev C1), the click on Firmware. Scroll down and you'll see that the latest is 3.12NA and has a download button, which points to the file in my link.
Now, I don't know why the update check in the interface doesn't work properly, but I doubt it's very accurate. It probably checks a list on some server that hasn't been updated in a while. It's always better to check by yourself using the instructions I described above.
To answer your question, theoretically it shouldn't create any problems and if anything goes wrong there are methods to recover. If the new firmware creates new issues, you can always downgrade back to 3.11NA.
To update the firmware, download the file I linked to to your desktop/laptop. Connect to the router over a WIRED connection (not wireless). Access the interface and go to Tools > Firmware. Under Firmware Upgrade hit Browse, select the file you downloaded and hit upload. Wait for the indicated time then reload the interface. Your settings you made in 3.11NA should be kept in the new firmware version.