1. I'm pretty sure that background checks work beyond doubt. I'm pretty sure that skills tests work beyond doubt. I'm less confident in AI resume/profile analysis and skills matching tools - both are getting better.
3. Agree, it's simplified, but for most companies, field and "hiring" managers are barely able to do an effective interview, let alone smoke out someone lacking interview skills from one lacking communication skills.
Agree both background checks and skill tests can work very well in an ideal form, but it's expensive (in time, mostly). As practised, they are very much a mixed bag. The latter is a problem past early career stuff anyway, as you aren't going to learn much in a couple hours.