A landfall ability triggers whenever a land you control enters for any reason. It triggers whenever you play a land, as well as whenever a spell or ability puts a land onto the battlefield under your control.

A landfall ability doesn't trigger if a permanent already on the battlefield becomes a land.

Whenever a land you control enters, each landfall ability of the permanents you control will trigger. You can put them   on the stack in any order. The last ability you put on the stack will be the first one to resolve (As a result, you can have those abilities resolve in the order of your choosing.).

Admonition Angel's landfall ability and its last ability are linked. The last ability refers only to cards exiled with its landfall ability.

If Admonition Angel's landfall ability triggers, but the Angel leaves the battlefield before it resolves, its last ability will trigger and resolve first. All previously exiled cards will be returned to the battlefield. Then the landfall ability will resolve and exile the targeted permanent forever.