• Is there API connectivity for the Site Review website?
• Is there an API on sitereview.symantec.com that would allow category lookups (without loading the webpage itself)?

There is not a public-facing API for the Site Review service.

There is a product called ThreatExplorer that does offer some API lookup functionality.  You can learn more from the following resources: 

• About Threat Explorer
• Getting Started with Threat Explorer

Contact your account team for further info about the ThreatExplorer subscription.