What is the ruling on one who abandons prayer under duress, and does that put him outside the fold of Islam, and what is the ruling on the one who compels him to abandon prayer?

There are two scenarios for coercion to abandon prayer: The first is preventing the worshipper from performing it even by gestures, and the second is coercing him to do something that is incompatible with prayer. This coercion removes sin and accountability from the worshipper, based on the Prophet's (PBUH) saying: "Verily, Allah has pardoned for my Ummah their mistakes, their forgetfulness, and what they are coerced into." He must make up for the prayers he missed after the coercion ceases. As for unacceptable coercion, it is when one can still gesture with their head or eyes. The coercer commits a great sin, as Allah Almighty says: {And Al-Fitnah (disbelief or Shirk (definition)) is worse than killing} (2:217).