Yes it can. If Chatot knows the move Chatter you can record a short sound. It is activated the same way as a field move, such as Fly or Cut.
Yes Chatot can Mimic your words by the move Chatter though it is a reason why it isn't allowed in Wi-Fi battling.
Yes, but it is a bit distorted once you record a sound. Its higher pitch. Anyways, how you do this is go to your party and click on your chatot and there is a chatter button. Its like using fly.