Are you trying to do a simple 1/3 1/3 1/3 split on the scenarios mentioned? If so, an AB test would suffice and just have each experience return a json property that you are ready to code for. As for the API call itself, the Target docs are pretty good on this front:
https://developers.adobetarget.com/api/delivery-api/#section/Getting-Started
Activity url is just something that you tokenize/hard-code in your API request so that Target knows if you are qualifying for a production or non-prod activity.