Skill scaling not clear enough

Example: Allied General (green)

-basic atk: Deals magic damage, damage scales off your MAX HP

Question, does its basic attack scale with MAGIC stat or only MAX HP stat?? Also does ATK stat add dmg to it at all?

ATK no. It should scale from HP, but it'd be easy enough to test. change one or the other and see if the damage changes significantly.

The Sentinel Allied General, as you said, has it's base damage relied on the Magic stat, but has an additional scale with HP.

They are visually seen in battle like: Magic dmg is blue, Physical dmg is red and True dmg is gray. So according with the colour you have the information of what kind of stat you must expect to scale with. So when the Basic Attack says Magic/Physical you are safe to go.

The damage can be random (magic, physical or true) as Soldier Eddie, but usually is stated which stat it scales of (SP for Soldier Eddie).

The only exception is when the damage is true and it don't tell anything about scaling. My perception until now is that it scales with the same stat that the other habilities does, but some characters are unclear.

A good example of true damage is Sentinel Souless Demon, which reads: deal true damage to all enemies, damage scales off your max hp. It really only relies on the max hp, and his damage output is not affected by buffs in-battle (+atk, +Magic), it really is the same damage accoding to the levels (enemy/character) and effectiveness, since it's true dmg.