For experienced projectors ONLY: I mean have you ever tried to find out the answer to something or seeked enlightenment or information on a subject in the astral about something here such as math for example or whatever...and been filled with information on the subject?
Yes (and multiple times in my life). However, I am not an experienced projector (e.g., I do not fit in the box that you present). But know that I did not have to classically project to get these answers from non-physical energy or higher beings or the higher self. I was simply accessing (through meditation, prayer, presence) something beyond my physical self (non-physical).
fwiw, I present this response, because your posed question presents such unusual limits upon the community here. We are all (and always have been) 'more than our physical bodies'. Even before we learn projection. Many come to learn OBE work or AP'ing with a well established spiritual practice in place and multiple experiences with the non-physical already. At least that is my own experience.
Yes. Information from the astral plane can be collected and carried over. Information can be collected from a number of subjects. Math, science, whatever. It is not limited to just school subjects, either. In my opinion, though, there are just too many awesome and informative lessons and experiences to be had while out of body. I'd rather not worry about my math homework while I am there. I prefer to ask those questions on this physical plane.