Sorta like tacking round and round.

I'm not sure how it would practically be done but I just imagine a disk (whew, spelled correctly this time..) shaped area always facing the sun, tilted towards the Earth to cancel the Earthward component of gravity.

But it's just an imaginary potential well and i'm not familliar with it's stability so i'll fudge and guess the would need to adjust and correct for perturbations while also facing the sun, mostly.

AND, an object in an orbit AND rotating would experience coupling between these two motions which also could throw the whole deal out of whack.

Solar storms, I don't know. As long as the disk isn't charged or has a magnetic field, and assuming the charged particles comming towards it are neutral on a scale
smaller than the disk, I don't know what would harm it. Photoelectric effect causing it to charge up maybe.......