Can you find studs thru exterior stucco or wood siding? Thanks

No, it cannot. This stud finder works best with drywall. If you're very patient and experienced using it, you can get *hints* from it that may help you locate studs through denser walls like plaster. But that's hit or miss. I've owned two of these sensors and used them daily on remodeling jobs since 2013. I know what they can and cannot do. They can reliably detect studs through interior drywall. Beyond that, it's hit or miss. Exterior stucco is too dense for it. Exterior wood siding is too dense. And note that exterior walls may contain metal lath or foil-faced insulation. That metal will confuse the stud sensor. Electrical wires and metal pipes will also confuse the sensor. Realistically, you shouldn't expect it to work for anything other than interior walls covered with gypsum drywall. Note also that these sensors aren't very durable. The internal electronics will be damaged if they're dropped onto a hard surface, so it's silly to call them "professional grade". They're just cheap plastic.

can this alert you to AC runs in t he wall?

no this sensor does not tell you where the ac runs are in the wall.

how well over thick second floor carpet

I have tried using this sensor on second floor thick carpet and had no luck locating joists. Great on sheetrock walls though. I don't think that there is any sensor that will pick up joists through carpet and plywood.

Will this detect studs behind plaster and will it detect wires?

Detect studs behind plaster? Yes!! In my 1930's lath-and-plaster house, it reliably detects studs - to my great relief after making about 12 useless test holes based on the readings of a Zircon stud-finder. This does not have wire-tracing at all, though, but there are other devices (dedicated and also combined with stud-finding, I believe) that do.