How exactly does Prime Axiom take initial ranged attacks but buy additional melee attacks?
Prime Axiom's Tow Cables have Drag. When a ranged attack with Drag deals at least one point of damage (remember, Puncture means you automatically do one point of damage), after the attack has resolved, including the push effect that Drag generates, you may make a melee attack against the model the ranged attack just damaged, which is independent of the push effect (so it works on models which cannot be pushed). Regardless of whether you elect to take this melee attack or not, Drag also allows you to buy additional melee attacks later (typically with focus), despite having chosen initial ranged.
This rule in no way bars you from buying additional ranged attacks, if you prefer, but remember that initials always come before additionals, meaning you should always finish your initials first. Here is an example of proper order:
Tow cable 1 (initial).
Melee attack generated from tow cable 1 (generated by Drag).
Tow cable 2 (initial).
Melee attack generated from tow cable 2 (generated by Drag).
3 accelespiker attacks (initial).
Buy accelespiker or fist attacks.
Remember that Sustained Attack triggers on every melee attack, including the ones Drag generates.
How do Colossals differ from other models when making ranged attacks while in melee?
A colossal can make ranged attacks while in melee. A colossal never suffers the firing in melee penalty when targeting a model it is in melee with. A colossal cannot gain the aiming bonus while engaged.
How does the Weapon Platform rule from Syntherion's feat impact the Prime Axiom?
The Prime Axiom can make all of its initial attacks, melee and ranged. The melee initial attacks can be used to make a power attack if necessary (and this does not use up your ranged initials, only your melee initials). If you make any additional attacks - that is to say, either buying additional melee attacks or buying any additional ranged attacks - you can no longer make any initials, so make sure to take all of your initials before buying others.
More importantly, the attacks from Drag are not additional attacks - this means that you can still harpoon drag in, make your drag attack, and still make any initial attacks (melee or ranged) you have left.
Source:
http://privateerpressforums.com/showthread.php?165245-FAQ-Convergence-of-Cyriss&p=2104842&viewfull=1#post2104842