dashboard light to replace catalytic converter, later engine loud dash light disappears

Not knowing the reason for the loud noise would disconcerting to me. Usually load noises from engine or any other system is a indication of a serious problem. I would definitely have a mechanic check it out. A catalytic check engine light to me would indicate the downstream O2 sensor detected a defective cat. This followed by a lot of noise then a absence of the check engine light afterwards could mean damage to that O2 sensor.

I think a new cat and both O2 sensor need to replaced and all the computer codes checked to find out why the cat failed in the first place otherwise the problem will reoccur.

The catalytic converter is actually a set of thin "tubes" like a square grid that has been extruded. This tube-like system improves the surface of the converter that comes in contact with the gases. With time, this "grid" crunches in a way that produces long "needle" like fragments. These fragments very often stuck in the grids holes preventing the air been exhausted properly, thus reducing power and even changing the sound of exhaust system. You should have your converter examined for such a case because this case, if worsens could lead to engine issues such as overheating, stalling, inability to start etc.