In US universities, how much academic information does a professor have about graduate students enrolled in his classes? Does he know immediately (from some internet / intranet access) which students in his classes are undergraduates, masters students, PhD students, non-degree students?  Does he typically have access to his students' transcripts, thesis work (dates submitted / approved / topic), and knowledge of his students' academic / research advisors?
At my R1 state university in the U.S., I do have info on whether students in my classes are undergrads or grads or non-degree, which are auditing and which taking it for a grade.

I have no information on their transcripts, nor thesis work nor status, nor academic or research advisors.

For students that are my advisees, yes, I have such information. In fact, for PhD students or MS students whose committees I'm or have been on (that are still active...), I do also have such information. But not for any other students.