The word "may" is used to mean "has the option to." For example, an ability that says "At the start of the Engagement Phase, you may perform a action," means that the ship has the option to perform the action, but can also decline.
The word "can" is used to mean "has the capacity to." For example, an ability that says "While you boost or barrel roll, you can move through and overlap obstacles" means when a ship with this ability boosts or barrel rolls, it ignores the rules that prevents them from overlapping or moving through obstacles. The ship always applies this effect as the effect is not optional but instead an expanded capability.
The word "must" is used to mean "is required to." Although all effects that are not "may" effects are mandatory, the inclusion of "must" is used to reiterate a mandatory effect that could provide a drawback to the ship with the effect.
Many abilities are restricted to occur "once per opportunity," which means they can be resolved only one time during the specified timing window. For example, if an ability occurs "At the start of the Engagement Phase," this ability can only be resolved once at the start of each Engagement Phase.
As another example, if a ship has the ability "While you perform an attack, you may reroll 1 attack die," it may resolve that ability once during each of its attacks.