Can outfield players go in the penalty area, and when is a penalty given?

Not without penalty. Under The FA's Walking Football Laws (February 2025), the penalty area (a 6m-radius semicircle in front of each goal) is for the goalkeeper:

• An attacker entering the opponents' penalty area: the defending team gets a goal clearance.
• A defender deliberately entering their own penalty area: a penalty kick to the opponents.

A penalty kick is awarded when:

• a defender deliberately enters their own penalty area
• the goalkeeper deliberately leaves their own penalty area
• the goalkeeper commits a sending-off offence in their penalty area
• a player denies a goal or obvious goal-scoring opportunity by handball (except the goalkeeper in their own area)
• a player denies an obvious goal-scoring opportunity to an opponent moving towards goal by an offence punishable by a free kick
• the opposing team commits its fourth "not walking" offence

Taking it: the penalty mark is 6.5m from the goal. The goalkeeper stays on the goal line until the ball is kicked; everyone else stays at least 3m away, behind or to the side of the mark and outside the area. The kicker starts with both feet on the ground no more than 2m from the ball and must kick it forward. Feinting once the run-up is complete earns the kicker a blue card.