Is it possible to get caller location by GPS?
Any mobile phone provider needs to be able to route calls to the correct tower to service a phone, so they must know to at least the location to the accuracy of the tower cell area. Generally speaking, this information is not available to parties in a telephone call.
An application can read the location at any time, and gets this as latitude and longitude. It is up to you to do a lookup of the city and country from this information.

Yes. A phone application gets location information as latitude and longitude, and the applications can simply exchange these values as strings over the data network.