DOORS NG has a project-wide type system. You can define an artifact (aka object) type and use it in multiple modules. In fact you can define an attribute (for example, an enumeration), and use it in multiple artifact types.  Note that modules can contain arifacts of multiple types (as well as having their own type with unique attributes on the module itself).

Project administration is done in the web client. See the "manage project properties" menu option under one of the icons in the very upper right of the page.

Your userid must have a DOORS NG Analyst (or RRC Analyst) license and have a project admin role.

The first level of security is whether someone has access to the project or not.  Within a project, team areas are used to manage access and other kinds of permissions; these can apply to specific artifact types and/or folder hierarchies. Then your users can be added to appropriate team areas.  Probably best to skim the help on this topic before you start creating team areas.

In the DOORS NG 4.0.1 release the optional rich client is primarily for authoring modules, editing them, and creating traceability among them.  Most other actions are exclusively done in the web client, or (in my opinion) generally best done there.

So comparing DOORS NG to DOORS as the product's exist today:
DOORS NG primary client: web
DOORS NG optional client: rich
DOORS primary client: rich
DOORS optional client: web (DWA)