I would like to start using the merge contacts API, but wanted to understand the rules first. For instance, what determines the winners and losers for properties? What happens to the losers in the merge process (e.g. contact record, property, activity, etc.)
I understand that there's a primary and the ID to merge, but don't know if that determines the winners and losers for individual properties.
By winners and losers, I'm assuming that you're referring to the primary contact and secondary contact, am I right? If that's the case, you may want to refer to this article for a better idea of what happen when you merge contacts: Merge contacts. There are some exceptions to this rule and I'd suggest for you to read through it.
As for the usage of the HubSpot Merge two contact records | Contacts API, the contact ID that is stated in the URL will be the primary contact and the one stated in the POST data will be the secondary contact.