Does equipement that gives a bonus to a characteristic (like Power Armour or a Flip-Belt) also increase the Characteristic Bonus?

For example, does Light Power Armour increase melee damage by 1 or does a Flit-Belt affect the character's Iniciative?

I'd say yes. After all, if your strength and agility are augmented by certain equipment, then it makes sense that actions you take based on that magnified characteristic would also benefit. If you get hit by a man wearing power armour then its going to hurt a lot more then if you simply were punched by the same fellow without the giant metal outfit.

Yes in all cases, but only AFTER Unnatural Characteristics are taken into account.

Maese Mateo said:

A flip-belt does not give a bonus to a Characteristic. It gives a bonus to certain Tests. Not the same thing.

(And IMO the bonus to "all" agility-based Tests is poorly thought through. It should only work on things like Dodge and Acrobatics, not Security or Pilot [starship]. )