Caserta I'll try to help you here as best I can. Hope I don't sound like a know it all, or confuse you more.
A converter changes 120v to 12v. An inverter changes 12v to 120v.
Unless a previous owner or the dealer, or you installed an inverter, you don't have one in your ERA. All your TV's are 12v and run off your 12v system in the van that the converter supplies. Whoops, that's right, the 70X only has 1 TV, the same info applies.
As far as charging the coach batteries. The generator is the least efficient way to recharge them. Most efficient of course is a 120v hookup, which goes through the converter which has a single stage charger built in that supplies a constant 13.8 volts to the coach batteries. Next would be the Sprinter engine while driving.
A heads up. One of the worst things you can do to a Sprinter engine is let it idle unnecessarily. After talking to a Mercedes engineer up at the Winnebago rally held yearly, this is basically what he said. It clogs up the DPF, (diesel particulate filter), and the EGR system, (exhaust gas recirculation). Either of these will trigger a check engine light, (CEL), and require a visit to a Sprinter dealer to repair these and/or clear the codes.
Any of the above charging methods take time. You can't recharge an AGM or wet cell battery when down half or more in 30 minutes. It takes hours. The chargers push a high amperage initially into them, then taper it down over time until they are full. The last hour or so is the top off time when they are down that low.
Another heads up, you should never run a wet cell or AGM battery down below 50% because it causes permanent damage to the plates and they'll never come back up to full charge. This is even the case with deep cycle batteries.
If your van hasn't been altered, you probably have either 1 or 2 AGM batteries as your coach batteries attached to the frame behind the rear wheels. AGM's are even more sensitive and can be damaged by improper charging or overcharging than wet cell batteries. They are VERY expensive to replace. $375.00 to $500.00 for the pair of them.
You probably don't realize this, but your chassis battery, for the Sprinter part of the equation, is in no way attached to your coach electrical system. You have to guard it to make sure you don't run it down accidentally by playing your dash radio, or leaving something turned on such as the cab courtesy lights or whatever. It's only charged, unless you install some kind of aftermarket charger such as a Trik L Charge, or small 110v low amp charger tied into your coach system, when you are running the engine.
One other thing I just thought of that you may or may not know, is that you should always start your generator either while the engine is running, or you are still plugged in to 120v and are getting ready to unhook. It pulls a BIG draw on those coach batteries. They are deep cycle, not starting batteries. Doing this will not hurt anything, or you, because of a built in transfer switch you have that prevents any feedback issues while doing this.
Hope this helps you a bit