To find whether Salesforce instance is Up and Active using API, then use https://api.status.salesforce.com endpoint.

Remote Site Settings:

Sample Apex Code:

String endpoint = 'https://api.status.salesforce.com/v1/instances/NA100/status';
HTTP h = new HTTP();
HTTPRequest req = new HTTPRequest();
req.setEndPoint( endpoint );
req.setMethod( 'GET');
HTTPResponse res = h.send( req );
Map < String, Object > fullMap = ( Map < String, Object > )JSON.deserializeUntyped( res.getBody() );
System.debug( 'Key is ' + fullMap.get( 'key' ) );
System.debug( 'Environment is ' + fullMap.get( 'environment' ) );
System.debug( 'Status is ' + fullMap.get( 'status' ) );
System.debug( 'Is Status Active? ' + fullMap.get( 'isActive' ) );
System.debug( 'Release Number  is ' + fullMap.get( 'releaseNumber' ) );