A whip can be used to make attacks against creatures up to 15 feet away, even if it doesn't threaten that area. The Bodyguard feat enables you to use aid another when an adjacent ally is attacked. The Aid another action says that you need to be in the position to melee attack against the opponent that is engaging your ally, it does not mention the requirement that you threaten that target.
No, because aid another out of your turn requires you threatening the enemy square.
Aid another requires you being in position to perform a melee attack against the enemy, which when not in your turn requires being able to perform an attack of opportunity. You need to threaten the enemy square to perform an attack of opportunity.
Whips do not threaten the area where they have reach, and threatening is a requirement for attacks of opportunity. Thus you cannot use Bodyguard with a whip unless you have a special feat or effect that allows you to threaten with that kind of weapon (as for example the Improved Whip Mastery feat) or somehow being able to use the whip as an immediate action.
There is an specific FAQ that clarifies this:
Bodyguard: The Bodyguard feat says that I can spend one of my attacks of opportunity to aid another the AC of an adjacent ally, but it doesn’t say one way or the other whether this removes other restrictions on aid another? Particularly, do I need to threaten the attacking enemy? Also, has that enemy provoked an attack of opportunity from me?
You still need to fulfill all requirements of aid another, including threatening the attacking enemy. Bodyguard uses up one of your attacks of opportunity for the round, but the enemy hasn’t provoked an attack of opportunity from you, nor are you making one (which is relevant for abilities like Paired Opportunist).
Bold emphasis mine.
Rules as Intended: Yes
The whip is treated as a melee weapon with 15-foot reach, though you don't threaten the area into which you can make an attack.
The requeriment of Aid Another is simply that you are in position to make a melee attack against that foe:
If you're in position to make a melee attack on an opponent that is engaging a friend in melee combat
Meaning that you can use Aid Another even if you have weapons that normally do not threaten adjacent squares, such as Unarmed (without improved unarmed strike) or the Whip.
Bodyguard is intended to require you only to be adjacent to the ally you're defending, not to require you to threaten their attacker. Requiring you to threaten the attacker makes the feat MUCH less useful, since then you can't block ranged attacks or reach weapons or attacks against targets with concealment or cover or anything else that would prevent an AoO. My intention with tying it to the AoO mechanic was simply to make it an ability you could use more than once per round, rather than wanting to tie it specifically to all the implied mechanics of AoOs. I had thought about just making it an immediate action, but that limits it to once per round and takes your im/swift action. I figured that was an appropriate mechanic for In Harm's Way, but the defensive bonus of AA was modest enough that I thought it entirely fair to not limit it that way.
As an side, I should say that for both feats, as well as the shield feats and shield-based archetypes I wrote, I thought that defender characters needed a little extra love in the rules, whether evil emperor bodyguards or altruistic protectors.
It's possible I had misremembered the mechanic for Aid Another, thinking that AA to add an attack bonus required an attack roll vs. AC 10 against the target while AA to add to AC required an attack roll vs. AC 10 against the defender. I can't really say for sure about my thought process 3 years ago, but that could have been the root of the problem.
- Jason Nelson
But is not the official ruling as has been answered on this FAQ.
Using a whip provokes an attack of opportunity, just as if you had used a ranged weapon.