While it will be possible to cut into the wires and build a device that will publish state and trigger the solenoid that opens the door, it's probably not a good idea.
Firstly you have no idea what voltages it all works at, it could very well be mains AC power.
You then have to design a network service that securely exposes the interface for the app (assuming mobile phone). This is most likely internet facing (definitely for an Alexa Skill) so needs to be done properly to stop just anybody opening the door.
There is also the question of the audio, that will need something more powerful than a esp8266 as it will need to do audio encoding/decoding in near real time then forwarded to the app.
So yes it is all possible, but probably not worth the effort unless you really like a challenge. You would be better buying off the shelf solution. I've not looked at combined systems but something like the Ring doorbell with camera and app deals with knowing who is at the door. Then a number of companies make smart locks, e.g Yale or Abloy.
And if you are truly mad you could always sign up for Amazons new Key service that lets Amazon let their delivery drivers into your house when your not there....