How many amps available to the 12v batt?

I can only speak to 05 Prius but doubt if there is much difference.
The auxiliary battery, judging by its size has an output of about 30 A/H (ampere/hours). Both auxiliary power outlets are fused at 15 A. Since Watts = v*a (volts times amps.) this calculates out to 15 * 12 = 180 watts each.

When working with (installing) electrical devices, the biggest danger is fire. At all times, when current moves from the battery, through wires to an appliance, the whole circuit dissipates heat. Stated another way, the battery, the wires and the appliance, heat up. A fuse in the circuit is actually a thermal switch that melts at a specified temperature thus interrupting the current flow.

Also the human ear can’t stand loud noise for sustained periods. Hearing loss is insidious, be careful.

 

To add additional perspective, the battery has a 150A fuseable link to the car's main electrical path, and the inverter output (or close to it) has a 100A fusable link.
Toyota seems to oversize the fuse in relation to the nominal current/wattage they rate the system for. Case in point, the outlets have a 15A fuse, yet are rated for 120W max, which is 10A. So, keep the draw from the inverter down to 80A.
80A*12V=960W minus any loads built into the car, such as the brakes, the computers, lights, etc.

Your battery won't last very long if you draw the max current out of it and the car is not in READY.