It is both and more. You can use it as L4 (per packet, half proxy) by applying a FastL4 profile to a Performance Layer 4 Virtual Server or L7 with a Standard Virtual Server with a HTTP, XML or some other L7 profile. You could also use an F5 as a L3 router and for forwarding at L2.
with regard to Partitions in BIGIP,there is only a default partition by name Common that is created. So, if a user is given Admin access, and if in that role he creates VS, pools, monitors, profiles, irules etc, all of them would be created in the same default Common partition, right?