1. it actually sounds like your House batteries are holding up very well over several weeks... there will also be draws on the batteries unless you PHYSICALLY disconnect them...you don't have the REMOVE them, just install a disconnect, found at any auto parts store, on either the positive or negative terminal of the battery 'bank'.
For the Chassis batteries, there should really be nothing to cause them to lose any charge if you are using the rotary 'main' disconnect... I've never had ANY issue with my steps or starting the coach, even after months of non use, and I don't even turn the rotary disconnect to the chassis batteries... 2) but, yes, the steps draw power from the Chassis battery bank, and are tied into your ignition.
3. I have 2 100w solar panels, and they seem to take very good care of the House batteries, on good sun days, when in storage, but I've never expected them to have anything to do with also charging the Chassis battery bank. The output of solar is probably not going to ever be enough to trigger the BIRD, if able, to output also to the Chassis batteries. I'm not even sure it would, in any case, since your Solar is simply going directly to the House batteries, NOT thru the BIRD.
enjoy... : )
'14 Palazzo 33.3 bunkhouse 34' diesel
KingTailgater2 Dish HD, 100w/5a SOLAR, BlueOx
100,000+mi since '14 - US, Alaska, Canada - Northwest, GA! (also, '14 Gulfstream Amerilite and '07 ForestRiver Rockwood) : )