My house is 60 years old. My shower is separate from tub. My shower drain has black water sitting in it. Is that a problem?
All drains have a trap to prevent sewer gasses from escaping into your house, so water sitting in the drain is normal. It shouldn't be black, but the pipes are usually opaque so it might appear black.
If you pour a bucket of water down the drain, it should drain quickly but leaving water in the trap. If it does not then you likely have a problem.
I suggest removing the shower drain grate with a phillips screw driver and try to remove any blockage on the top and then try to pour some water down the drain to see if it is still a problem.