Creating own entity types in Jira - extending data model

To all developers of Jira plugins and extensions - is it possible to extend Jira data model with my own entity types? I mean add totally new entities (database entities) to the system but with assumption that they will have relationships with existing Jira objects (users, issues, projects)?

And if so, few more specific questions:

1. can we ORM-map the entities into standard SQL tables, or some special data storage structure has to be used?

2. Is there any support for such extensions in the Jira SDK? Or any examples that would illustrate how this is done in the SDK?

3. What about the UI - is it possible to use Jira's UI components to build custom forms? What about list search functionality, Lucene indexes, filters - possible to reuse for custom objects?

4. Examples or relevant documentation?

Thanks!