If the Skie server is down, do the rules still apply on devices?
Yes. Rules are cached on the device and keep working offline, so the filter, app lists, schedules and hardening carry on with the last verified policy. What pauses is new information: changes you make and reports from the device queue until the connection returns.
Enforcement happens on the device, by Android itself, because Skie is the device owner. It does not need to ask a server before blocking an app or filtering a site. That is the reason the same logic covers a tablet in a basement classroom with no signal.
Policy bundles are signed and kept on the device. During an outage, the device keeps applying the last bundle it verified. Schedules continue, because windows are stored with days, start, end and allowed apps. Offline mode, with its own allowed apps and an organisation maximum, ends by itself when the network returns.
What you lose is freshness. Changes you make in the dashboard during an outage reach devices once the connection is back. Reports wait too, and devices show older last seen times until they check in again. When it returns, devices sync quickly and retry if the first attempt fails.
The gate is the one thing to remember. If a device has not synced within your Due limit, an overlay on unlock tries to sync first, and gates only if the sync does not finish. Set thresholds and sync intervals with this in mind.
If Skie as a company were ever unavailable, devices would also keep their last rules. Skie does not speculate beyond that, and you can end management with Remove Skie while you still have access. For a pilot, switch a test tablet to airplane mode for a day and see for yourself.