"Welcome, team! You will have to solve these puzzles all by yourselves, as I won't be giving any hints over the radio."

Because the host is addressing a "team" (multiple people), the plural reflexive pronoun yourselves is required. "By yourselves" means "alone" or "without help."

"Oh, and if anyone gets scared and wants to leave early, just know that the exit door will lock itself automatically."

"The exit door" is an inanimate object (singular), so we use the pronoun itself.