motorhome solar system question

In order to figure out battery needs, you should have a handle on loads in terms of total watt-hours and maximum instantaneous wattage, and an objective for time before needing shore power or generator. In mobile applications, space can be a limiting factor. That said, if you will just be relying on batteries for 12v lighting and phone charging, a couple of deep cycle 12v batteries may work fine.

A 12v panel would typically put out 17-18v in full sun and reasonable temperature, and you would see ~50odd volts if 3 were wired in series. Seeing 100v from the string, and the rating of 300w each, suggests they aren't 12v. If so, you will need an MPPT type controller to charge a 12v bank.

Car starting batteries are designed to deliver high currents for a short time and then be almost immediately recharged. They don't generally work well as house batteries. Using them would also mean putting them in parallel, which can be difficult to keep balanced (especially if the batteries have varying health to begin with).

Those are "24 V" panels. You need an MPPT controller to get the maximum power out of them for a 12 V system. What controller do you have now?

With your 3x245w panels you can support around 300 amp hours of 12v batteries. You don't want to run them down more than halfway on a regular basis, so you have around 1800 watt hours for loads on battery power.

A 2000w inverter will use a fair bit of power just being on, so you may want to keep it turned off when not needed, and avoid running it just to charge a phone or other small load. The speakers and sub may take a lot of power depending on volume etc.