My Palazzo is a 2014 so not sure this advice is true to you.
1 - Your chassis battery is supposed to charge up when you are charging your coach batteries by shore power or generator but I am not sure about solar. I suspect the same. However I occasionally get a brief low voltage warning when I start my RV and it goes out in 3-4 seconds. If the RV cranks easily I would not worry.
2 - It is normal for the airbags to deflate and then reinflate when you start up.
3 - Your chassis battery should be charging your house batteries when you are underway. If not something is wrong with the relay system that routes power to the battery systems, on mine a BIRD/Trombetta system. The generator should not have to run, but if for some reason your house batteries are low I guess it would kick in even if underway.
4 - I looked at replacing the headlight but decided not an easy retrofit and did not
5 - On towing just be sure the vehicle does not exceed your RV tow capacity, both for pulling and braking reasons.
6 - Congrats on your new motorhome.
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