Short answer
HubSpot's KB: every data sync app has field mappings that decide which data syncs and in which direction. Not all dropdown properties can sync two-way; some map one way as text. Owners sync by email address and must exist as users in both apps. If the other app has one name field, the first word maps to First Name, and both First and Last Name mappings must be on.
1. Data integration
The data integration page in my demo portal.
2. Field not listed
Check the type rules in the KB: a field only maps to compatible HubSpot property types.