No. TeamCal runs in your web browser. On a phone, you can add it to your home screen so it opens like an app (step 4 of the quick start checklist on the Welcome page).

Everyone with a TeamCal sign-in, the wall display, and any intranet page an Admin has placed the embed link on. Nobody outside the company has a sign-in. Avoid putting sensitive personal information in event notes.

Not currently. TeamCal is a shared team calendar; keep personal appointments in your own calendar, alongside the TeamCal feed.

No. The feed is one-way, from TeamCal to your calendar app. Make team changes in TeamCal.

30 days. An Owner or Admin can restore them from Settings → Backup → Recently deleted.

TeamCal records who added each event and who changed it last, so the team knows who to ask about it.

Yes. Sign in on each device. Changing your password signs out your other devices.

Ask an Owner (who can manage Members) or an Admin (who can manage every level) on your team.

Very little. It refreshes itself, reloads nightly, and shows a banner if information becomes out of date. If the screen restarts, open the browser in full screen again.

An Owner or Admin on your team first. For anything they can't resolve, or for suggestions, use the contact form.

TeamCal is hosted by TeamCal.us, not a large cloud provider, and your team's calendar runs as its own separate install with its own database. See Ownership and security.