Hello Diane
Yes the church is still there...Opposite what used to be a fine hostelry, The Golden Cock. I doubt if there will be a head stone, most patients were only afforded a simple, pauper type funeral.
You may try contacting Anne Littlewood; author of 'Storthes Hall Remembered'. She is the expert on all things to do with the hospital.
If you type the name of her book in goggle you will find her website. Anne is incredibly approachable and always willing to help.
May I wish you and yours the best for the festive season.
Paul