With version v4.2 and above we do have a CORBA component for our iControl communication. We include only the CORBA components necessary to support our listening service.
For the OS, you are going to have to check with support if you don't know which one you have. In the past we have been mainly BSDi (which has very limited java support) and a couple of products in the past have used FreeBSD but I don't currently believe that any of them are on FreeBSD as of today.
For the memory, the exact specifications of the product depends on which platform and options were picked so I can't comment on the amount of memory installed as it varies.
And for development, F5 does not support external software being installed and run on a F5 device. Our devices are highly tuned for their configuration and any external software can adversely effect the performance of the device as a whole. CORBA for instance has a huge memory footprint requirement for applications.
If you need detailed specs on the products available and our official support policies, I'd suggest you contact F5 Technical support directly as I cannot speak for our device support group. We are here to support external development of applications using iControl.
F5 Technical Support
Email: support@f5.com
Phone: 206-272-6888
Web: http://www.f5.com/support/
AskF5: http://tech.f5.com/
Just for my own knowledge, what were you planning to do with CORBA applications running on the BIG-IP?
-Joe