Är Vår planet står i fara också tänkbart?
No, är i fara is an idiomatic expression. I'm sure people would understand står, but it's not a phrase any native Swede would use.
Perhaps you were thinking of 'står i brand' as in Hela skogen står i brand (the whole forest is on fire).
"Faran! Faran! Will Robinson!Sorry, my age is showing, but it does help me remember an important word to know.