Correct. Inverter getting its input from wires on the truck battery, outputting to a 120v charger clamped to the house battery.
You first need the inverter to be big enough in watts to run the input watts of the charger when the charger is doing its full amps. Next you need the truck system to be able to hold the truck's own voltage up while carrying that inverter load too.
Yes, you should have the converter output going to the fuse panel and also the house battery going to the fuse panel so either one can run the DC circuits. That also puts the converter on the house battery using the same path in reverse from when it is a path from battery to fuse panel. meanwhile, the 7-pin connection goes to the battery, not necessarily to the fuse panel first.
7-pin charging (DC) has nothing to do with the converter charging of course, which needs 120v to run the converter.
I have a picture of my inverter charger method when I was trying that a few years ago but in this new case I would want to have it all inside to do the truck camper instead of here doing the trailer batts.