I understand that the C-8 Pro offers cloudfree support.
Exactly what entails "cloud free".
Are you able to control your devices via your phone's Hubitat app even if the internet is down?
Are you able to control your devices via your Amazon Alexa or Google Home even if the internet is down?
Are you able to control your devices via any other method even if the internet is down?
Please explain?
You don't need the mobile app to control devices at all (there is a local web-based interface, among other methods), but a quick test with no Internet still loads the Light/Switches tab in the mobile app for me. I imagine Dashboard might too with proper DNS, but part of my test took that away too. 
Alexa and Google Home likely both need Internet to process voice, and both integrations ultimately rely on cloud endpoints in general, so that is unlikely to work. I believe Amazon is trying to add more local options to Alexa and perhaps Google is too, so this may change in the future, but possibly not. Hubitat itself can't escape these constraints, and along these lines, it should be noted that it cannot magically remove the cloud from the few devices that inherently require it for functionality, either, like Ecobee.
As an alternative, HomeKit works locally, as will Siri in conjunction with HomeKit on devices that support local voice processing like recent iPhones (older ones only need Internet for voice processing; the Hubitat communication is still local).
Local Dashboards, whether a traditional Hubitat Dashboard or the newer Easy Dashboard, also work locally, as, again, does the regular admin interface.
All Hubitat hubs are this way.
Yes, as long as your local internet and/or router are working. You would have to also be on your local network hardwired with a desktop/laptop, OR on your local Wifi with a phone or laptop which is on the same network as the hub. You could use any internet browser (again on the local network) or the phone app as long as mobile data was shut off to force things back to your local network.
On the other hand, you cannot be remote, like at work, and have the internet go down and still control the hub via the app. Many people also don't think to shut off mobile data and have trouble connecting to their hubs in an internet outage when at home, that won't work as it is trying to go through other's servers (like Verizon) and not exclusively on your internal network.
These are cloud based devices and integrations. There are others similar to this as well where you can bring things into Hubitat, but the main processing lives within the cloud.
Anything cloud based will fail to work if they can't reach their servers. I would not rely on using these whenever possible, and in the future devices that could operate completely local if possible.
For example, having smart bulbs with no physical control (I.E. a switch) where you cannot shut them off without someone's cloud server would defeat the purpose of a local hub. Instead, use dumb bulbs with a Zigbee or Z-wave smart switch that talks completely local.
Many people recommend smart switches with dumb bulbs whenever possible. It gives you full local/physical control, plus the benefits of being able to smarten things and operate them remotely or via an app.
With other devices, you sometimes don't have much choice. You are stuck using a browser or app to do things like change RGB colors on a strip, even if the protocol is local, like Zigbee or Z-wave would be on this hub. Or you rely on the cloud for something like Alexa, but who wants to argue with Alexa about changing color or brightness on a bulb?
In the case of some of my devices, I have no smart features if the internet goes down. My hot tub is this way, it turns back into a dumb device where I have to push buttons on the machine itself to control it. And I am OK with that, it isn't a "mission critical" device.
I was trying to decide what you were asking here. What I think you are asking is the following.
Cloud services are need to:
Cloud services are not needed to:
A blend of the above:
My guess would be that this is referring to the "CloudFree" badge in the advertisement:
The Home Automation Features and Benefits | Hubitat Elevation Local Home Automation – HUBITAT page has some additional details; in particular, the graphic at the bottom titled "Hubitat Elevation® vs Cloud Dependent Solutions", which might help answer some questions.
Download the Hubitat app
