Short answer
HubSpot's KB: the connected (integration) user's Salesforce permissions determine what HubSpot can do there; HubSpot's changes are performed as that user. Before changing it, make sure the new user has equal or higher permissions. Each HubSpot account connects to one Salesforce instance; several HubSpot accounts can each connect to the same instance.
1. Connected apps
Connected apps in my demo portal.

2. Sync rules
See sync rules.