Exported Video Has Unsynchronized Tracks

Did you preview your project in Shotcut by pressing space? Was it aligned there?

I’m not sure what you mean. If you mean there are gaps between clips, you right-click empty space and pick ‘remove’ like at 1:07 in https://www.youtube.com/watch?v=pXdgg3mGpec

If video and audio of videos are out of sync (lips moving, voice coming too late or too early), then this thread might help you: Audio Aligns With Video In Shotcut, But Goes Out Of Sync After Export