If you are not in close combat then you take the monster reaction test at the end of the phase in which the rider or crew are killed. If you are involved in close combat the rules clearly state that the test is not taken until after the combat is entirely resolved. If the monster is victorious in the combat, then it states to take the test in the first turn when the monster would be free to move and act normally. If you lose a combat and flee, but are not caught by the enemy, the book is silent on when to take the test. If we use the timing of a victorious monster as a guide, then the test should be taken the first turn when the monster would be free to move and act normally. Therefore, in cases where the monster loses a combat and flees, take the monster reaction test at the beginning of the turn after it rallies.

It depends on which reaction you roll. Also remember that the monster only performs actions in the owning players turn. So for example if a result of 1-2 (monster runs away) is rolled then it will be applied in the owning player's compulsory movement phase. If a result of 3-4 (monster charges) is rolled then it will be applied at the declare charges step in the owning player's movement phase. If a result of 5-6 (shooting / guarding the body of its master) is rolled then it is applied immediately but will only come into play if the monster has a ranged attack or breath weapon and an enemy unit is within range during the owning player's shooting phases.

No.

These units do not count as skirmishers even though the models are not ranked up. When determining what the unit can charge, or for the purposes of flank/rear charges by enemy units, use 90 degree arcs centered on the monster itself. When the unit is in close combat, it forms up following the rules for skirmishers - ie those in range get into base-to-base contact, those our of range form up behind. The models in the unit move at their own Movement value as long as they remain within 1" of each other. Also note that any character allowed to join the unit counts as "riding" the monster for the purposes of any special rules they may have. For example, if a Dark Elf Beastmaster joins a War Hydra unit, then it does get to ignore Monster Reaction tests if all the "crew" are wiped out. View Monsters & Handlers.