Many consumer devices which accept an external microphone will provide "plug-in power". This is a small voltage typically from 1 to 5 volts across two of the contacts in the microphone connection.
Apple and (most) Android devices are no exception. Most use a 4-conductor TRRS connection with the following pin-out:
TIP = left headphone out
RING = right headphone out
RING = ground
SLEEVE = mic in + plug-in power
The plug-in power is usually around 2V on smartphones and is supplied as +2V on the microphone (sleeve) conductor. The phone will only supply it if it detects that a microphone is in place, which it does by testing the resistance across Mic to Ground to see if it's consistent with a microphone's impedance - something like 200 to 5000 ohms impedance, and I hear the iphones can be very fussy with this and need very close to 1600 ohms.
This means the maximum power you could draw from this and still seem like a microphone would be pretty small - around 1.25 milliamps. There are some low powered microcontrollers or other devices you may be able to power with this.
Note that plug-in power may be a similar concept to "phantom power" as used in pro audio gear but it's a different and incompatible standard. "plug-in power" is what causes the tiny electret microphones in smartphone headsets to work without needing their own small battery.
As for how to actually exert control over your attached device from an app, that's getting into much more complicated electronics. Presumably it is possible if you use the left and/or right headphone out lines to send signals to the device.