Tarc does not currently have a dedicated "offline mode" feature. This page explains what actually works without a connection today, and what doesn't.
Guest Mode stores all progress locally on your device and doesn't require a server connection to function — in that specific sense, a guest using the app after it has already loaded can continue a lesson without connectivity. This is a side effect of how Guest Mode is built, not a dedicated offline feature.
If you have an account and lose connectivity mid-session, there's currently no guaranteed local queuing/retry system for changes made while offline — the safest assumption today is that an active connection is needed for your account's progress to actually save.
Partially — Guest Mode can continue a lesson that's already loaded without connectivity, since it's fully local. Signing in, Cloud Sync, and the leaderboard all require a connection.
Not available yet — there's no background sync or offline queuing system for signed-in accounts today.
Not currently — no service worker is registered, so the web app doesn't have offline caching in the way some installable web apps do.