[bellaCuba]

Well...You've had a fun couple days. To begin, the rattle you hear in the cat area is probably the guts breaking down. It's like a honeycomb looking stuff in there. This would be the 1st thing I'd address, because as the cat breaks down & the "honeycomb" breaks up, it sometimes starts clogging the exhaust. Pieces may also get caught in the baffles of the muffler.

In regards to the #32 EGR code, you may be able to do some bench tests and also clean out the exhaust port on the EGR valve. Sometimes the pintle becomes so caked up with carbon, it doesn't allow it to move or blocks the port. You may want to pick up a new gasket for it. Sometimes the old one will tear on you. The new one can be reused a couple times, like if you got a new EGR valve to install. Also check your vacuum hoses to it & all around. Not enough vacuum will also keep the EGR from working.

To check the diaphram on the EGR, use a vacuum hand pump and pressurize it (sucking) to no more than 6 psi. If it holds, then the diaphram portion is ok. I think you should also see the pintle move up & down when using the pump.

Are they all connected to you're battery issue? Probably not. Just all happened to come about or noticeable to you at the same time. Post an update with your findings, so that this tthread can help others in the future. Or if you have more questions... Good luck with everything!