Can smartphone apps place calls ?

Might be possible, in theory, for some smart phones - playing a prerecorded sound isn't that difficult, however, I don't know whether an appropriate path from the (any) audio source to the telephone uplink would be possible for every phone.

What would be almost trivial to do would be to send an SMS or any other kind of text (or internet) notification. The only downside of this: the phone (i.e. its main processor and the sensor(s) you want to evaluate) must be switched on, which will drain the battery rather rapidly (i.e. in several hours).

Quite a bit less power consuming would be to evaluate the currently used phone network cell - that part of the phone is running continously anyways, but will only be accurate to within a few hundred meters (10....5000, depending on the area). Actually, my phone's firmware uses this to determine whether to switch on WiFi in order to save power.

Yes its possible. I am an app developer. This is where permissions come into play