From what I can tell by looking at the notification code, yes it should show notifications from subareas too. However, it looks like there is a problem if you have subscriptions for multiple nodes if those nodes would trigger notifications for the same event.
It appears that only the first subscription that is found in the database would be used, when in fact you would expect the most qualified subscription to be used. In this case, if the most qualified subscription is used and it's not configured to trigger an alert, then the user would not receive one. However, due to the current broken stacking, if you have a different kind of notification selected for one or more of these stacked subscriptions (such as weekly email), it's possible that it would not trigger an in-site alert simply because the wrong subscription is used to send the notification.
I have to do some more investigating to determine just how unexpected the behavior can become, and what the best way to correct it would be.
As for notifications of the entire wiki, it's not clear if it's related to that issue or if notifications just don't reverse all the way up the chain back to the index (I have a feeling it only works as expected for scheduled emails, if at all).
If your default subscription mode is not being honored, then of course it would be compounding the first problem I mentioned. If it's really not being followed, then this is the first thing to fix since it will make debugging easier if fewer subscriptions are being made and it's important not to make users angry by auto-subscribing to things that they intended to be opted out of.