I have a PD Converter and power distribution panel. When I start my Generator, nothing happens for 30 to 45 seconds and then a timing relay powered by the generator actuates and provides power to the transfer switch. The TDR can and in many cases is a solid state potted devise without any mechanical relay parts. When the transfer switch engages, the generator out put is TRANSFERED to the converter and the shore power connection is opened. Some RVs require that you manually transfer the input power by plugging the shore cable into the generator output. In your case, however, it seems you have a transfer switch.
I am not on top of the new Inverter/Chargers, I have an older distribution panel with a PD 9245 converter with a charge wizard. Not having any experience with other brands is kind of limiting but I am assuming they all work very similar.
There is a member on the forums that tinkers(repairs) converters. I don't know his name but someone must have it.
As far as your other questions, the time delay in the transfer circuit is not receiving power. Either your generator is not producing power or there is a problem with some part of the time delay relay circuit. You can check for generator power at the terminal of the TDR, or the generator outlets.
No charging with the batts disconnected.
The DMM is your friend and you can check a lot of things with it.
The article "The 12 volt side of life", may have a schematic of the converter/inverter. Look that up or Google for RV converter TDRs.
