1. this is sewage leak, don't bother looking for other sources.
2. the leak is at the junction between horizontal 4 inch black pipe (shown in the top part of the last picture) and the vertical pipe , hidden behind the drywall underneath the cut ceiling. If I guess correctly this vertical pipe is
an older cast iron pipe. The horizontal section of the black pipe is the source of problem because it trapped a small amount of water to keep the top of the cast iron pipe wet and leads to rust in the long run.