I've been wondering how often #1 happens. Our coding test isn't particularly difficult but it is timeboxed, and somehow candidates pass it who take 15+ minutes to string together a for-loop when they come on-site.
Home based unsupervised coding tests are fine I think, as long as you ask the candidate to talk through their solution when they come in to meet in person.
I've received a mistaken "please come in for an interview" email intended for someone else. The recruiter was embarrassed when I illuminated the error. I enjoyed knowing I was "not selected to proceed", even if it was by mistake vs the usual silence.
