[INFO] Bitrate settings

[Selur]

The black & white source is 4:2:0. Advanced Video Coding, Main@L3.1 CABAC / 4 Ref Frames. In that case, would that need more data going to color?

If you look at the Vapoursynth Preview with split YUV ('Compare view' enabled, 'Filtering->Vapoursynth->Misc->Preview->Split Compare View' enabled and set to 'splitYUV&interleaved' (or just 'interleaved') ), this way you can see what happens in the chroma.
If the black&white has no chroma data it's basically 4:0:0 an modern encoders will nearly drop the chroma planes, thus when you add data chroma is will need to be compressed.

Does going 4x3 to 16x9 letterbox same resolution (just adding black bars to the left and right) require more data or is it negligible, because the black bars doesn't require much data?

black bars should be negligible (especially if they are at macroblock / mod16 borders)

So for a 1000kbps 4:2:0 640x480 25fps to 1920x1080 letterbox 50fps mp4, a 5000kbps would be a good target? (using average bitrate 1st pass)

Just reading 'average bitrate 1pass' I would say: No, using 1pass bitrate encoding is a dumb thing.
But assuming the amount of details scales with the pixel density, it should produce similar quality.
Instead of guessing bit rates, I would recommend doing a few 1 pass crf encodes (16-23) and see what prefers the quality level you need.

Final question. Does setting the target at 5000kbps require more or less computation time than 2500kbps or its the same?

More, assuming CABAC or similar encoding methods are used, which all newer formats do.

Cu Selur