Lots of questions. Here are some answers:
Chargers are a lot less expensive per amp of charging
capacity than inverter/chargers. So make your decision based on utility vs cost. A stand alone 1,000 watt Chinese made inverter
might cover limited inverter
needs and they are cheap
A Honda 2000 will only put out 13 amps continuously. A Freedom 25
inverter/charger (100 amp charging
capacity) pulls as much as 20 amps while charging. So that big of a charger won't work
So it is best to size the charger or inverter/charger to match the Honda for maximum charging capability. Some are more efficient than others. For a stand alone charger, the Iota
55 amp is very efficient and just meets the 13 amp limit.
Yes you can plug
in your shore power cord to the Honda.
But if you have room, consider more solar panels
. The Honda plus Iota
is going to cost $1,200+. You can buy a lot of panel capacity plus a new controller for that much money