I don't know the name (have only handful of cacti), but have few suggestions. Brownish bottom looks like corking, and that is normal for many cacti. But smell doesn't sounds very good. I would unpot it - it may be difficult to take it out of that recurved pot - and check the roots. They could be damaged. If so, they could regrow if plant is healthy enough. It jwould need to be potted in different pot and probably different mix (one that drains well). The color doesn't look right either. Rotting plant could send out new shoots, so if main plant is sick, it tries to 'replace' itself. They could be left where they are, or if original plant is sick, they may be potted separately.

As for pot, it is much better to use regular pot, plastic or other, that is not recurved. Attached saucer is also not allowing for good drainage. I had few of the same type, and threw them out..