Of your three qq
this is the most interesting,
and I agree with WWW, that it is not settled.
The first step in this was Raymond Dart describing Australopthecus in 1924 (Taung child), and thereafter the bitching back biting and general name-calling started.
If you could find a direct ancestor, then after a lot of argy-bargy you could estimate the time of divergence.
The big thing over the last few years (one of them) is that the recognition (and that includes reinterpretation of things like Dart's original excavations) is that Homo Sapiens and the others co-existed - so one did not give rise to the other.
I think Dart was asked about this, just before he died, and said, oh yeah we thought that in 1960. but knew if we printed it, they would all call us mad.......