I believe they're using the shindou version for all regions because the shindou sound effects can be heard in the trailer. If so, it will be practically useless for serious runs.

Is it known which character is objectively faster for this category? The world records for each are close with luigi being a few seconds faster, but the mario run having some minor mistakes. I couldn't find any TAS runs for the category either. I know for every other category, mario is faster, but this is the only one where they're relatively close.

Original nes controller using a usb adapter is your best option, especially if you plan on switching to console in the future. Raphnet is known for making great quality adapters, but since this is only NES, a cheap dumb adapter from tomee should work just as well.