A WordPress multi-site or “network” would fit your need exactly. One thing to point out based on your example. You may only choose sub domain or sub folder installation. WP multi-site is not geared to do both by default, you must choose one or the other at setup.
The setup is surprisingly simple:
http://codex.wordpress.org/Create_A_Network
Regarding themes, yes. Plugins and themes can be managed separately across all sites in the network. You could easily have 2 dozen domains (or subdomains) running on a single WP multi-site, each with it’s own theme and plugin set.
Additional questions regarding security: Yes – each site has the ability to grant users with varying levels of access. You may also create additional “Super admin” users which can manage all sites on the network. You can add and remove privileges for users for each site or across the network.
Safety is about much more than user access. This arrangement does give you control over all types of user access, however.