How can encode video with images like these (overlay a video over a fixed image) with ffmpeg?
To overlay a half-sized version of a video in the center of an image, use

ffmpeg -loop 1 -i image -i video
-filter_complex "[1]scale=iw/2:-1[ovrl];
                 [0][ovrl]overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2:shortest=1[v]"
-map "[v]" -map 1:a -c:v libx264 -c:a copy output.mp4




To frame the video:

ffmpeg -loop 1 -i image -i video loop 1 -i frame
-filter_complex "[1]scale=iw/2:-1[ovrl];
                 [2][ovrl]scale2ref=iw*1.2:-1[fr][ol];
                 [fr][ol]overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2:shortest=1[fv];
                 [0][fv]overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2:shortest=1[v]"
-map "[v]" -map 1:a -c:v libx264 -c:a copy output.mp4


If you composite the frame onto the background image beforehand, in ffmpeg or elsewhere, you can just use that resultant image with the first command. Of course, you'll lose freedom of movement for the video overlay.