Some additional info.
First, these settings are all documented at https://learn.microsoft.com/en-us/mem/intune/apps/app-protection-policy-settings-ios.
Next, some answers to the direct questions posed:
does it mean that every 30 minutes, intune will check device activity
No. Activity/inactivity is app specific, not device specific. It's actually a bit more nuanced than that though as the activity timer can be shared by multiple managed apps that shared the same APP. The following note from the official docs (linked previously) sums this up fairly well:
"Note: On iOS/iPadOS, the PIN is shared amongst all Intune-managed apps of the same publisher. The PIN timer for a specific PIN is reset once the app leaves the foreground on the device. The user wouldn't have to enter a PIN on any Intune-managed app that shares its PIN for the duration of the timeout defined in this setting. This policy setting format supports a positive whole number."
If there is no activity on the device after 12 hours, it will ask me to authenticate.
No, as noted, this is app specific as these are "app" protection policies. Apps have no way of detecting activity at a device level.
If I don't respond to the authentication, my access to Outlook will be blocked for 12 hours (Offline grace period)?
No, that's not what the offline grace period signifies. As @EE-9037 calls out, the offline grace period is the amount of time the app is allowed to run in the foreground while it is not connected (for whatever reason) to Intune (since all apps that are APP aware communicate with Intune directly to download APP policies). Thus, this says that an app where this policy is applied is allowed to work without connectivity for 12 hours and then will be locked from further use.
If I don't use Outlook on my phone for 365 days, it will delete the data on my Outlook on my phone where my corporate email is associated?
Correct.
If this is correct, what happens to the users' access after a weekend?
Nothing specifically. There's nothing special about a weekend. For anything to happen, the user would have to actively using the app while not connected for 12+ hours. Then, as soon as the connection is re-established, the app would be unlocked, and functionality would be returned. The question here is why they wouldn't have connectivity over the weekend?
Will they not be able to access Outlook on Monday and have to wait after the 12-hour block is done before the next authentication or PIN request?
No, as noted, that's not what the grace period is. Unblocking has nothing to do with the grace period, unblocking is based on connectivity. If the app never loses connectivity, the grace period is irrelevant. Even if they do lose connectivity (once again for whatever reason), they would have to be actively using the app for a total of 12 hours for it to block and 365 days for it to wipe.
Does inactivity mean user opening or using Outlook?
As noted, it means the apps targeted by the policy being in the background and not having focus on the device.
What if user does not open Outlook for 12 hours but is actively receiving emails and calendar alerts on the phone?
Nothing. As noted, the 12 hours is only significant if the app isn't connected and the user uses the app for 12+ hours.
Do they count as an activity?
Receiving e-mail and calendar alerts does not constitute activity. This is app specific.