Can we start from the beginning? This is terribly confusing.
Whatever the source video was, the converted 1280x720 result is now a 16:9 widescreen format with square pixels. If the source was 4:3, there are probably black bars baked into the left and right sides now.
Where did these come from? Are they an upscale of the 1280x720?
Rendered out which file? The 1280x720, the 1920x1080, or the original videos (whose resolution and aspect ratio are unknown to us so far)?
The next problem is that “DVD (SD NTSC)” is a 4:3 output format. If the timeline is “DVD Widescreen NTSC” and there are 16:9 videos added to the timeline, but the export is 4:3, then Shotcut will shrink the 16:9 timeline to fit inside the 4:3 output. This creates black bars on the top and bottom that will be baked into the output video file. Notice what happens if we bring the exported 4:3 file back into Shotcut (which is still in 16:9 timeline mode) and put a green color clip under it:
We can now see that the top/bottom black bars are baked into the 4:3 video due to the aspect ratio mismatch during export. Meanwhile, the sides are green because there is no video data there when playing back 4:3 video on a 16:9 screen. Without the green clip underneath, the sides would default to black, creating the thick black border around the video that you noticed before.
Probably use the “DVD (SD Widescreen NTSC)” export preset instead of the other one, assuming your source videos are 16:9, which is still unclear. This one change will probably fix everything, but I wanted to walk through the process in case it doesn’t, to make troubleshooting easier.
This should not be the case. If using the “DVD Widescreen NTSC” video mode, Shotcut should be exporting frames that are 853x480. This is the final resolution after 720x480 (with non-square DVD pixels) has been scaled into 853x480 (with square computer pixels).
When everything is set up properly, there should not be any cropping required whatsoever.