How do you cap an old toilet in a basement?
A building supply or good hardware store should be able to sell you a toilet cap to bolt in place of a toilet with a good gasket to keep out smells and avoid back ups.
There is a blockage in the waste line. Have you flushed the basement toilet to see what happens? Try running the upstairs shower and see what happens. (use two persons , one up stairs, one downstairs so you can control the amount of water that rises in the toilet.) There should be a "clean out" cap somewhere downstairs near the point where the waste line exits the house. It is here that one would "snake"…
How far can the toilet be from the basement drain. The toilet will be installed on the main floor but is there a certain degree angle for the pipe to be from toilet to basement drain?
The toilet is the lowest point, fluids seeks the lowest level, other sewage is coming up through your basement toilet. The system might be installed wrong or there is a blockage in some discharge pipes. Call a plumber, it can be really bad, when I was a kid we had our whole basement flooded with two feet of raw sewage after a big rain storm.