Irresistible Faefolk

Irresistible Faefolk's controller is the attacker. Irresistible Faefolk reaches the battlefield before its triggered ability can pull the enemy unit.^383.2.c It contests that battlefield for its controller because no one controls it and it was not already contested.^190.3.a.1

Its ability then pulls the enemy unit there. With opposing units now at the contested battlefield, the next cleanup marks it for combat.^319.8323.8 When that combat begins, Irresistible Faefolk's controller is the attacker and the pulled unit's controller is the defender because Irresistible Faefolk was the unit that contested the battlefield.^{466.2.c.1466.2.c.2}

No. A move is defined as a permanent changing its position from one location on the board to another.^448.1 When you play Irresistible Faefolk, it enters the board from a non-board zone (such as your hand), which is a zone change, not a move.^448.2

Yes, removing Irresistible Faefolk by itself does not stop the enemy unit from moving. Removing Irresistible Faefolk is not a counter instruction.^426.1426.2.a Its already-finalized ability remains on the chain and executes like a spell.^407.5

Irresistible Faefolk's trigger condition identifies the battlefield it moved to, so the ability records that battlefield when it triggers.^359.3.f.3 Removing Irresistible Faefolk later does not erase that destination, so the chosen enemy unit can still move there when the ability resolves.