Hhmmmm....part of the problem may be the quality of the original, at least for the frame one. I see that some lines are heavier than others, and some lighter or darker than others (like a photocopy maybe?). But even so, you should be able to get a better scan.
For the record though, no, Trace Bitmap is not intended to accurately reproduce images. In a black and white line drawing like that though, you should be able to get a pretty darn good trace. Where it fails badly is like on photographs such as a landscape or a family photo.
According to the settings you reported, you're doing a Single Scan using Brightness Cutoff. The problem with that one is that the Preview Update feature doesn't work. In all the others, you can click the Update button to see what the current configuration of settings will look like. With Brightness Cutoff, you have to click Ok to see the preview, and then Undo. Then you can change the threshold, and click Ok. And continue to adjust it, remembering to Undo inbetween attempts. You should be able to find some threshold value that will fairly closely resemble the original.
Or you could try Edge Detection, where you just have to click Update to see how changing the threshold will affect the trace. Just adjust threshold then click Update to see how it looks, etc. until you find the best one. I don't think Color Quantization will be a good choice in this case, but experimenting can only help you learn
However, I would not suggest any multiple scan option for this particular image.
Also look at the Options tab of the Trace Bitmap dialog. You can try different threshold values for Smooth Corners, or maybe even deselect it, for the frame. Just remember to keep doing the same Ok, Undo, change value, Ok, Undo, etc. as long as Brightness Cutoff is selected on the Mode tab. I'm not sure if the Optimize Path setting will have any effect on the frame, but you can experiment.
For the flower, all 3 of the settings on the Options tab could come into play. And I suspect you can adjust the Smooth Corners and/or Optimize Paths for that one, and get something better. But since you couldn't show that result, I can't be sure. Also on the flower, you might find Edge Detection will give a better result.
I know it can be frustrating and confusing trying to get a good scan. If you reach the end of your patience, and you don't mind posting the full size of the frame I don't mind experimenting a little. The flower one might be harder because of all the shading. And finally, here's the manual info, where you might pick up some helpful tips: http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Trace.html