Check engine light.

Factual Questions
#1

So, my check engine light came on. I went to the local Autozone, ran the code and changed out the front O2 sensor on my 2001 Honda Odyssey Van. I cleared the code by disconnecting the battery for a short time, started it up and everything seemed fine. Two days ago the light comes back on. I go to Autozone and it runs a P0420 code which suggest the Catalytic converter needs changing, or Oil is leaking into the exhaust, or vacuum leak, or misfire.
The engine runs fine, there is no smoke coming from anywhere so that takes care of two of the possibilities. How do I check for a vacuum leak? Or do I just need to replace the catalytic converter?
Also, the battery has recently begun to get weak and will need to get a new one in this weekend. It’s approximately three to four years old. Could this be related to my problem. When I had a dodge truck that the battery was going out I was getting all sorts of bells and whistles going off before I changed it out.

Any help is greatly appreciated.

#2

A vacuum leak won’t set that code. An exhaust leak near the rear O2 sensor might.

The overwhelming probability is that the catalytic converter is faulty. Field experience has shown that aftermarket converters usually don’t work properly (the code will reset), and the reliable fix is a genuine Honda converter.

The battery has nothing to do with it.

ETA: A faulty rear O2 sensor could set that code. That sensor’s operation should be tested before taking a chance on a converter. Reading codes alone is not always sufficient for complete diagnosis.