Branch analysis is available as part of Developer Edition.
Status vs Quality Gate
The same quality gate that is applied to the project as a whole is automatically applied to long-lived branches as well. This is not editable.
Issue Creation and Synchronization
During the first analysis only, issues (type, severity, status, assignee, change log, comments) are synchronized with the Main Branch. In each synchronized issue, a comment is added to the change log of the issue on the long-lived branch: "The issue has been copied from branch 'master' to branch yyy".
Then, at each subsequent analysis of the long-lived branch, any new issue that comes from a short-lived branch automatically inherits the attributes (type, severity, ...) the issue had in the short-lived branch. A comment is added to the change log of the issue on the long-lived branch: "The issue had been copied from branch 'the short-live branch' to branch yyy".
Because long-lived branches will persist for a long time, you are likely to develop and release multiple versions from it, and so you can change the Leak Period of a long-lived branch in Administration > Branches.
Settings and Quality Profiles on Branches
Branch settings and quality profiles default to those set for the master branch, and by design, it's not possible to configure other values.