To clarify, you will still need to own a Corona for 3ds Max license and a Corona for Cinema 4D license, for the GUI part of the license (to be able to see and control Corona in the app). As it happens though, the associated rendering part of the license should not be tied to one or the other, so by owning one Corona for C4D and one Corona for 3ds Max, you should be able to use either version to render on two machines at once (so long as no other machines are using the rendering part of those licenses).
Correct on a machine being able to connect directly (so long as the Chaos Licensing Server is installed of course) and check the status of the licenses, so you won't need to VPN in to the office or anything. Of course if you left the office machine rendering, then when the home machine connects, it will find the license is in use already :)
And correct, so long as existing subscriptions are kept renewing, the same render nodes and pricing is kept.