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Yes. The farm runs at 24× real time, so a farm day is about an hour. When you open the app it catches up on everything that happened while you were away. Crops that are ready wait in the field, and a long absence never ruins the farm: after a while it simply idles until you're back. A farm manager keeps things running for longer.

Your farm is saved on your iPhone and, if you're signed in to iCloud, synced to your private iCloud storage. Sign in with the same Apple Account on your other device and the farm follows you there.

To keep things fair, the catch-up is checked against Apple's iCloud server time. If you were offline or not signed in to iCloud, the catch-up is limited until the app can confirm the time. Connect to the internet and open the app again, and the rest is added. Changing the device clock doesn't speed the farm up.

Check Settings → Notifications → Agriculture Farming Simulator and make sure notifications are allowed. The game holds alerts back at night, sends at most two an hour, and bundles alerts that are close together, so a quiet phone doesn't always mean something is wrong.

They use Game Center. Sign in under Settings → Game Center to appear on the leaderboards. In-game cash is never sold for real money, so the leaderboards stay fair.

Open the settings (the gear button on the farm) and tap Delete Account. This permanently deletes your farm on this device and in your iCloud storage, and you can start a new farm afterwards. It can't be undone.