No you're not getting it.
The A8 would be the default operating mode, and run iOS apps. (Actually the A7 is already more powerful, with higher GeekBench scores, than the perfectly fine 2009 MacBook c2d 2.2ghz I'm typing this on.) Most iOS apps will come up instantly - iOS MS Office, Mail, small games, videos, iMovie etc. Most non-power users would stay in this mode more or less all the time, with limited access to the file system.
When a demanding app is launched eg FCPX, Creative Studio, Photoshop etc or a heavy game, or Windows in emulation or a power user wants the OSX ecosystem then the Arm brings in the Intel chip to deal with that side of matters.
So I'm guessing that work will be divided between the two chips on a per-app basis, with iOS apps running on the Arm and OSX apps running on the Intel. As to the core underlying OS, I have no idea, but it would make sense to minimise the weight of the OS so as an educated guess the default will be the Arm, and elements of OSX will only be activated as necessary to support OSX apps / as desired by power users.
Some work would be needed to sort out the glue between the two sides, but the two OSes already have similar underlying filesystems and roots. iOS devs could continue writing code and updating their apps like nothing's changed, and ditto for OSX devs.
I would imagine a recompiled but identically functioning OS X will run on ARM devices and that iOS apps will only run within a development environment, allowing the apps to be run instead of present simulation.
They are not designed for cursor input.
Apple's own apps will be recompiled on day one for the ARM machines and if Intel apps run at all, and it's likely they will it will be through Rosetta-like software emulation. There will not be duplicate hardware (such as an Intel CPU) which would require the bulkier, louder, older fan-based hardware design.
Over the duration of the 1-2 year transition apps will be rewritten to run natively on the new quad/octo-core CPUs.
Present Intel apps will run slowly when emulated hence why a low end iMac or MacBook are the candidates for the first product. Pro's won't buy one to rely on for their work.
OS X and iOS will not merge on a user level but codebase similarities will permit universal applications at the backend.
I also say earlier on this thread that I think GPUs are part of the reason behind the rumoured transition: https://forums.macrumors.com/posts/19150268/