With gas engine, yes. Not sure about diesels.
Diesel, yes
Yes, legally and for the computer to function correctly you will need a catalytic converter.
That is the sensor after the catalytic converter.
Yes, your 2003 ram diesel has a catalytic converter. The converter is located under the cab.
Yes
On a gas engine there is one on each side of the catalytic converter. The diesel doesn't have any.
Yes.
That is the downstream O2 senosr and it located after the catalytic converter on the passenger side
NoNo
No.
Muffler should be after the cat.
If someone has not removed it, Then yes it is before the muffler.
In 2001 the Ram 2500 diesel did not come with a cat. it has a resonator and a muffler. the thing under the cab that looks like a cat is actually a resonator. so no they are not required