Is Apple still fixing the MacBook Pro backlight issue for free?

Check the exact model under Apple menu > About This Mac before you go anywhere. The classic sign of the cable problem is the "stage light" effect, uneven bright patches along the bottom edge of the screen, often only once the lid is opened past a certain angle. If that matches, ask the repair shop specifically about the flex cable. Some will just quote you a full screen otherwise.

Almost certainly not now. That programme only covered some 13-inch 2016 models, and only for four years from when they were first sold, so it's long run out. Worth asking an Apple store anyway, they do sometimes help as a goodwill gesture, but don't count on it. Apple's fix is a whole display assembly, which isn't cheap. Some independent shops repair the display flex cable instead, which is the part that actually fails.