Situation:

A vehicle is in base contact with an enemy trooper. As one of these units is a vehicle, neither is 'engaged', but they are in a melee.

Can a unit outside of this melee shoot a ranged attack at the vehicle?
Can a unit outside of this melee shoot a ranged attack at the trooper?

Some of the rules I found, but I'm still confused.

16.
"There are two types of attacks: ranged and melee.
» During a ranged attack, the attacker and defender are not in a melee, and the attacker can use only weapons that have a blue range (󲉬, 󲉭, 󲉮, 󲉯, 󲖀, 󲉰) icon."

40.
"While a trooper unit is in a melee with another trooper unit, those units are engaged. A unit that is engaged cannot perform moves, cannot be displaced, cannot perform ranged attacks, and cannot be targeted by ranged attacks, except from area weapons."

52
"Melee represents close combat between opposing units. When two miniatures from opposing players’ units are in base contact, those units are in a melee. • If two trooper units are in a melee, those units are engaged. Any unit type can be in a melee, but only troopers can be engaged. • When a unit performs an attack against a unit that it is in a melee with, that attack is a melee attack. "

Reread the entry from pg. 40 you quoted:

18 minutes ago, lologrelol said:

A unit that is engaged cannot perform moves, cannot be displaced, cannot perform ranged attacks, and cannot be targeted by ranged attacks, except from area weapons.

Being engaged is the only thing that prevents a unit from performing ranged attacks or being targeted by ranged attacks.

18 minutes ago, lologrelol said:

While a trooper unit is in a melee with another trooper unit, those units are engaged.

Only Trooper units can be engaged.

What about “When a unit performs an attack against a unit that it is in a melee with, that attack is a melee attack.“ ?

11 minutes ago, Mokoshkana said:

What about “When a unit performs an attack against a unit that it is in a melee with, that attack is a melee attack.“ ?

That's a good point of clarification that I should have made. If two units are in melee with each other, they can only perform melee attacks against each other, even if they aren't engaged. This is in the page 16 entry and the page 52 entry. A good example of this is the AT-ST. If it is in a melee, it can make a melee attack against whatever it is in melee with, and also use Arsenal 2 to perform a ranged attack against something else.

26 minutes ago, Lochlan said:

That's a good point of clarification that I should have made. If two units are in melee with each other, they can only perform melee attacks against each other, even if they aren't engaged. This is in the page 16 entry and the page 52 entry. A good example of this is the AT-ST. If it is in a melee, it can make a melee attack against whatever it is in melee with, and also use Arsenal 2 to perform a ranged attack against something else.

What about page 16?

16.
"There are two types of attacks: ranged and melee.
» During a ranged attack, the attacker and defender are not in a melee,

Attacker and defender are not in a melee with each other

4 hours ago, SailorMeni said:

Attacker and defender are not in a melee with each other

Where is the "with each other" part?

53 minutes ago, lologrelol said:

Where is the "with each other" part?

That's clearly what it means, even if they left out those specific words for brevity's sake.

59 minutes ago, lologrelol said:

Where is the "with each other" part?

If it isn't intended, then the rules regarding ranged attacks (performing or being targeted by) while "Engaged" are unnecessary. Since it is explicitly stated under the Engaged rules, we can infer that being in a melee does not innately remove a unit's ability to use ranged attacks.

1 hour ago, lologrelol said:

Where is the "with each other" part?

Even if they didn't intend for that to only include units that were in melee with each other, the only other situation it would preclude would be a unit that is in melee but not engaged performing a ranged attack against an enemy unit with which it is not in melee but is in melee with a different unit but not engaged.

"The attacker and defender are not in a melee" uses AND logic, not OR.

2 minutes ago, Lochlan said:

Even if they didn't intend for that to only include units that were in melee with each other, the only other situation it would preclude would be a unit that is in melee but not engaged performing a ranged attack against an enemy unit with which it is not in melee but is in melee with a different unit but not engaged.

"The attacker and defender are not in a melee" uses AND logic, not OR.

Or even a worse situation:

"During a melee attack, the attacker and defender are in a melee, and the attacker can use only weapons that have a red melee (󲉫) icon"

That sentence doesn't say explicitly "with each other" either, so by the logic that that is not implicit, a trooper unit in melee with a vehicle can perform a melee attack on an enemy trooper unit on the other side of the board which is in melee with another vehicle 🙂

I'm sorry, but the rules aren't implicit in their wording.

The "with each other" needs to be added, because someone said I couldn't shoot at a character in melee with a destroyer droid.

53 minutes ago, lologrelol said:

I'm sorry, but the rules aren't implicit in their wording.

The "with each other" needs to be added, because someone said I couldn't shoot at a character in melee with a destroyer droid.

The rules are clear enough, the rules from Page 40 regarding engaged troopers is explicitly the only instance that prevents you from shooting at a unit that is in Melee but must also be engaged.

There are no rules at all that say you cant perform a ranged attack at a unit that is only in melee.

Whomever the someone is that told you that you cant shoot into melee at all was wrong, it would appear that person does not know the difference between just being in melee and being in melee and engaged.