Terminals: Wherever on or immediately adjacent to the 12V battery you can find a solid point of contact with plenty of surface area. There may be a more clever location elsewhere, but I was just aiming for underneath the two main nuts that hold the main wires onto the battery. There is enough threads above that and a bit of room, so a lug should fit stacked with the car's lugs.
Order: Doesn't really matter, just connect to the inverter first and turn the inverter off before connecting and use an inline fuse near the battery just in case. I've heard reccomendations to do the negative first so you can't connect the other cable to the chassis (which is all on the negative terminal), but if the inverter is switched off it shouldn't matter.
Refrigerator, Clarity is just about the right size. Sump pump, if it's a ¼ HP or smaller one that only draws a few hundred watts, should also be fine.
Heater, though, not going to happen, you need to buy a larger dedicated generator for that. And that'll be true regardless of whether it's a portable resistance heater (probably ~1200W) or the blower on a central gas furnace. Or use a catalytic propane heater, but I hear those stink, somewhat literally.
The Clarity is a great solution for rare/catastrophe-level emergency power, but only for small loads.