Cisco Intersight API interactions can be encoded in XML or JSON and require an API key in the HTTP header for authentication: This statement is true. Cisco Intersight APIs support both XML and JSON formats for API interactions. API keys are used in the HTTP header to authenticate requests.

UCS manager API interactions are XML-encoded and require a cookie in the method for authentication: This statement is true. Cisco UCS Manager APIs typically use XML for encoding interactions, and a session cookie is required for authentication after an initial login request.

Cisco Intersight API: Uses either XML or JSON formats and requires API keys for authentication.

Cisco UCS Manager API: Utilizes XML format and relies on session cookies for authentication.