We don't disclose the operating system that our platforms run on. As you say, it really is not relevant as we provide a closed box system which is transparent to the users using it. Let's just say that we've written our own, highly optimized, intelligent, modular and scalable architecture that we call TMOS that runs the core of our processing. Do a web search on "TMOS" and "F5" and you'll find more information.
As for access control, currently our iControl interfaces are tied to the user policies that govern our Administrative GUI. We currently allow admin (full access), operator (read + partial write), and guest (read-only). We are currently working on expanding the features with a more extensive authorization model in one of our upcoming releases.
As for custom encryption, I'm not quite sure what you mean. Is this in regards to our management interfaces, or traffic level encryption. For our management interfaces, we transport everything over SSL and there really is no option to customize this. As for traffic level encryption, we offer full extensibility in how you configure and deploy. Our devices are a full proxy so we can proxy client-to-device and device-to-server. Also, this is configurable at runtime by making use of our iRules scripting language. And, since you have full control of all traffic content (including the payload), you can decide to partially encrypt the content in full or parially. A good example of this would be if you wanted to not allow credit card numbers outside of your enterprise. You could write an iRule that scanned all traffic for patterns matching valid credit card numbers and either mask out, encode, or encrypt the numbers. It's very flexible stuff.
Hope that answers your questions

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Joe