If a permanent spell tries to enter as a land during its resolution (for instance, a Clone entering the battlefield as a copy of a Dryad Arbor or an animated Mutavault), it is put into its owner's graveyard instead of entering. It never enters, so abilities that would have triggered on it entering won't trigger.

In Two-Headed Giant, triggers only once per upkeep, not once for each player.

Land can't enter, so an effect that "puts a land onto the battlefield" won't do anything, and the land will stay where it is.

If you cast a spell or activate an ability that lets you put a land onto the battlefield, the effect fails. You'll still do everything else the spell or ability tells you to do, such as shuffle the library.