Short answer
HubSpot's KB: the integration syncs records, sales orders and financial data. NetSuite needs REST Web Services, OAuth 2.0 and Server-side RESTlets on, steps there are done by a NetSuite administrator, and connecting users need the HubSpot sync role. You need a Data Hub subscription to create custom field mappings.
1. Connected apps
Connected apps in my demo portal.

2. Status field
NetSuite's Status field has its own setup article in the sources.