As to #4, “12v” solar panels often go up to 20-22v with no load and make the most power when run at 15-18v depending on the intensity of the sunlight so fully charging a battery to 12.6v is no problem. Look at the “Voc” and “Vmp” ratings of the panel you are using to confirm this. Voc= voltage with an open circuit, Vmp= voltage at maximum power point