Individuals... CFI / grade1 / grade2 .... confident / over confident / capable / cocky ... you cant compare nor judge them because of the title, you could presume but as you said, you had a skitish CFI, most automaticaly presume the CFI is the man! been around long enough to know that aint the case. Maybe less capable but still a good CFI.
Pvt / CPL students while training... no difference re solo, either ready to fly a helicopter solo or they are not.
Autos... some instructors shoot a decent auto early on however teaching it or helping a student learn to shoot one is a different story, constant evaluation and time instructing all other sequences gives them time to learn how students behave under pressure and better prepares the instructor i guess... i know instructors who will probably move on and never teach an auto to the ground, only forced landing sequences.
Also, from what i see out and about, most autos are controled re wind/surface etc making it as safe as possible to teach the basic fundimentals, and are tested on those during their test. So how long? we would hold them off at least until they get past the direct/indirect supervision periods and see after that if they will or not... its not a given thing. Properly?... define what you would call properly and may give u a different answer.
Good student? hmmm one who listens learns, does his home work, producing every thing required, meaning he has a good attitude, good student.
Hopefully then move on to being a good pilot.
Is that what your looking for?