This has the supertype world. When a world permanent enters, any world permanents that were already on the battlefield are put into their owners' graveyards. This is a state-based action called the "world rule." The new world permanent stays on the battlefield. If two world permanents enter at the same time, they're both put into their owners' graveyards.

If a cost includes life gain (like Invigorate's alternative cost does), that cost can't be paid.

Effects that would replace gaining life with some other effect won't be able to do anything because it's impossible for players to gain life.

Effects that replace an event with gaining life (like Words of Worship's effect does) will end up replacing the event with nothing.

If an effect says to set your life total to a certain number, and that number is higher than your current life total, that effect will normally cause you to gain life equal to the difference. With Forsaken Wastes on the battlefield, that part of the effect won't do anything. (If the number is lower than your current life total, the effect will work as normal.)

The loss of life from targeting this card does not work until after this card enters, so you can counter it without losing life.