Just be polite, as for standing on graves, occasionally it is necessary and allowed, best thing is to go in as if you were photographing anything respectful and use your manners, if you are worried about superstitious nonsense, I'd imagine a graveyard is not the place for you. If you can, you will find Saturdays the quieter day, not a lot of chance of a funeral and less visitors to graves on a Saturday. If you see a grave open and the earth dug up besides it is covered in grass matting there is a very strong possibility of there being a funeral that day. The grass would not usually be left to be stolen or blown away. If the grave has earth next to it but un-covered, it is probably dug in preparation for burial next day or so.
There are some lovely ornaments of beauty in a graveyard so enjoy, its very rewarding....