Good observation about right and left handed- pick your corner accordingly.
As for permission- At a high school, to be honest- I rarely ask. There's usually a newpaper guy or 2 around, who wander anywhere they want with an on-camera strobe- I am less of a problem than they are, and if I am asked to move, of course, I will. I make sure that I am not acting like a parent or fan- no cheering, etc. and I have never been asked to move. At this point, most of the coaches, Refs, and AD's know who I am am, so issues have been rare. If I am in a new gym and wanted to be thorough about things, I may ask permission from whoever seems to be in charge- that may be a coach or an AD- although if you don't know who the AD is, it may be hard to find them, if they are there at all.
Long story short- I would act in a professional manner, go where I need to be, stay out of the way of the game, and move away if I am asked to. Asking an AD for permission makes them responsible for you if they approve it, and I suspect that few would want that if they just met you.