Yes.

You've read the rules correctly and a weapon does indeed always do at least 1 damage more than its written rating when it hits, before subtracting soak.

Why?

As with other game systems that use similar mechanics (Shadowrun's net hits are very similar to uncancelled successes) the game rewards a good attack roll with increased damage. This makes sense in simulationist terms as well: the good roll represents a particularly lucky shot hitting a vital spot or similar.

While this mean that a weapon does always do higher than its listed damage it's quicker and easier to calculate damage if you don't have to remember to subtract 1 each time.

I have not been able to find anything about it, either.

However, the adventure module Onslaught at Arda I has some example Duty payouts. The amount is usually 3 or 5, depending on how dangerous it is to do something.

For example, saving fellow Rebels from an Imperial assault gives 3 Duty for someone who has the Duty (Personnel), and Duty (Space Superiority) gets 5 for defeating an enemy ace.

There are two examples of what I'd call a pittance duty:

• Duty (Resource Acquisition) gives 2 Duty if you find and recover mining equipment
• Duty (Tech Procurement) gives 2 duty for every dozen items from a weapons cache returned to the Alliance instead of kept for personal use

Using this as a base-line, I see it as follows:

• 2 Duty for a head-nod to your duty. It takes very little time or though, mostly just a quick transition scene
• 3 Duty for something that takes time in a time crunch, or requires a roll or two, but isn't exactly life-threatening
• 5 Duty is when you either succeed or die—well, not exactly die, since that's really hard to do. But it puts you, your team, or your expensive starship in real danger

Granted, all of this is just in my opinion, so take it with a grain of salt.