None of these are standard idioms - they are simply abbreviations used by that school. I have no idea what P and HP mean. High placement?
I assume that the parenting classes teaches parenting skills. Often, I've heard, these courses involve having the student take care of eggs, or dolls, or even high-tech dolls, so that they can't be left alone and must be fed and changed and so forth. Hopefully, it shows them the hard work side of parenting and not just the cute baby side, so they are more responsible about using birth control.
Driver's ed is driving lessons, yes. It includes both classroom on on-the-road lessons.
his/cul/geo - no clue. Cultural studies, perhaps?
Planar solid geometry? again, no clue. this is not any sort of idiom.
Immunizations - yes the student got his or her last vaccines on May 25, 2005.
A proficiency test is to see how well you learned to do something. S may be satisfactory.
I can tell you a lot about high school, but with things this school-specific, you'd better off asking the school guidance counselor.