I would like to obtain the current status of the quality gate for my projects in SonarQube via the SonarQube web api, but I do not see quality gate as
You can retrieve what you want with the "quality_gate_details" metric. As an example on Nemo: http://nemo.sonarqube.org/api/resources/index/?resource=org.codehaus.sonar:sonar&metrics=quality_gate_details
[{"id":48569,"key":"org.codehaus.sonar:sonar","name":"SonarQube","scope":"PRJ","qualifier":"TRK","date":"2014-11-30T16:13:17+0000","creationDate":null,"lname":"SonarQube","version":"5.0-SNAPSHOT","description":"Open source platform for continuous inspection of code quality","msr":[{"key":"quality_gate_details","data":"{\"level\":\"ERROR\",\"conditions\":[{\"metric\":\"blocker_violations\",\"op\":\"GT\",\"error\":\"0\",\"actual\":\"3.0\",\"level\":\"ERROR\"},{\"metric\":\"critical_violations\",\"op\":\"GT\",\"error\":\"0\",\"actual\":\"15.0\",\"level\":\"ERROR\"},{\"metric\":\"test_failures\",\"op\":\"GT\",\"warning\":\"0\",\"error\":\"\",\"actual\":\"0.0\",\"level\":\"OK\"},{\"metric\":\"skipped_tests\",\"op\":\"GT\",\"warning\":\"0\",\"actual\":\"0.0\",\"level\":\"OK\"},{\"metric\":\"coverage\",\"op\":\"LT\",\"warning\":\"\",\"error\":\"80\",\"actual\":\"81.5\",\"level\":\"OK\"},{\"metric\":\"test_errors\",\"op\":\"GT\",\"warning\":\"0\",\"error\":\"\",\"actual\":\"0.0\",\"level\":\"OK\"},{\"metric\":\"sqale_effort_to_grade_a\",\"op\":\"GT\",\"warning\":\"\",\"error\":\"0\",\"actual\":\"0.0\",\"level\":\"OK\"}]}"}]}]
For now, to get a full list of metrics, you can browse the "metrics" database table. Feel free to watch https://jira.codehaus.org/browse/SONAR-5378 that should make the detailed list of metrics available directly on the SonarQube web interface.
Since SonarQube 5.3 you can get the Qualitygate Status using the API: http://[sonarhost]/api/qualitygates/project_status?analysesId=[ID]
Since SonarQube 5.4: http://[sonarhost]/api/qualitygates/project_status?projectKey=[key]