Provenance of terraforming materials.
You mention getting things from the asteroid belt. There may be an easier way. Since you can move cargo fast (0.1c) you can afford to get the cargo from farther away. Asteroids are generally rocky with possibly some ices on top. Moons of Saturn are generally icy with some rocks in the middle.
There are a lot of moons of Saturn (and the moons of Uranus and Neptune are probably good targets as well). Collectively, they have far more ammonia and water than you could ever use to terraform a planet. So why not simply drag a few small to mediums sized moons of a gas giant into orbit around your planet and prepare to send them down?
Refining
Something not mentioned is the need to refine the materials. If you want the proper elements to be added to your moon in a matter of decades, then you have to be careful about what you add. Like any good culinary creation, you must measure your ingredients carefully.
You ingredients are bits of and/or whole moons. So how do you measure them? You have to melt them. You can utilize fractional distillation to melt away the various compounds. If you slowly cook (heat) a comet, all the Carbon monoxide will melt first (68 K), then methane (~91 K), ammonia (195 K), carbon dioxide (217 K) and finally water (273 K). All those temperatures are pretty far away from each other, so simply melt the ice ball slowly, and then separate the solid bits from the liquid at each step.
Now you have a set of liquid or slushy balls in space. If you were smart, you would do this far from the sun, so the carbon monoxide and methane will refreeze for you before transport. You now have a bunch of ice balls of reasonably pure compounds ready to go smash into your planet!
Recipe List
In the comments you say you want a plant with about 0.75 Earth's radius and mass; and 0.7 Earth's gravity. That doesn't work exactly, but going with some numbers that fit the bill more or less, let us assume your moon has radius 0.9 Earth's, density 0.8 Earth's, to get surface gravity 0.72 of Earth's. Mass ends up being 0.58 of Earth's.
Since surface area is proportional to radius, squared, we will need about 80% of the Earth's atmosphere, oceans, and biological matter. An atmosphere will need 20% oxygen and 80% inert gas; nitrogen is the most common inert gas and should do nicely. The requirements for our moon will be $3.3\times10^{18}$ kg of nitrogen and $2.1\times10^{17}$ kg of oxygen. The ocean will need $1.1\times0^{21}$ kg of water (though this could vary widely, depending on how wet you want the planet). Lastly, the biosphere will need at least $1\times10^{12}$ kg of carbon.
To provide these ingredients, we can add three compounds primarily. Ammonia can be used to generate atmospheric nitrogen; Carbon dioxide can be transformed in to atmospheric oxygen; and water is just water. At the ratio of two Ammonia per one diatomic nitrogen and one carbon dioxide per diatomic oxygen, our shopping list is roughly:
- $1\times10^{21}$ kg water
- $4\times10^{18}$ kg ammonia
- $2\times10^{17}$ kg carbon dioxide
The great thing about these ingredients is that they are three of the most common compounds in the outer solar system. They also provide plenty of surplus material for making a biosphere: Carbon Dioxide has extra carbon and ammonia has extra hydrogen. No need to add methane, there are plenty of fossil fuels to go around!
How to not make a mess
The next challenge is to not make too big of a mess when you deliver your materials. Here are the various factors you outlined.
How not to significantly damage the moon's surface
Without an atmosphere, your moon will likely have a surface covered in fine regolith similar to what covers Luna and Mars. If this surface is hit by impacts from space, the dust will end up mostly settled back into the surface. So from this perspective, there isn't too much to damage done by hitting the planet with space snowballs; the holes will be filled by dust (relatively) soon after impact. Lunar regolith has a density about 2/3 of lunar surface rocks (and Earth rocks), so the holes will be filled with a material that will be reasonably solid.
Newton's depth approximation for impacts is $$D\approx L\frac{\rho_i}{\rho_p}$$ where L is the length (or diameter, if spherical) of the projectile and $\rho_i$ and $\rho_p$ are the densities of the impactor and planet, respectively. Note that this approximation nowhere includes the velocity of the impactor. Let us assume that planet has a similar crust density to Earth (2500 kg/m$^3$), while the delivered volatiles, such as CO$_2$, water, and ammonia each have densities less than 1000 kg/m$^3$.
Assuming we want to limit impact depth to 200 m so we don't make craters too large, we can throw objects up to 500m in diameter at the surface without making too much of a mess.
How not to not make a debris cloud
Putting stuff back into space will both anger your space-junk-OCD Chief Engineer and represent a loss of materials. We don't want to do that. How can we avoid it?
First, we have to figure out escape velocity of our planet. From this post, we see that radius and density are both proportional to surface gravity. As calculated above, we have radius 0.9 Earth's, density 0.8 Earth's, to get surface gravity 0.72 of Earth's. Mass ends up being 0.58 of Earth's.
Escape velocity is calculated here as $\sqrt{2gr}$, where $g$ is gravity and $r$ is radius. Given the factors above, escape velocity of your moon is 0.8 of Earth's, or 9000 m/s. To ensure nothing goes into space, we will make the average ejecta velocity from our impact craters no more than 4000 m/s.
In this post, I perform calculations on the height of an ejecta plume. This model calculates ejection velocity as a function of distance from the impact site. We want the ejecta velocity at the edge of the impactor to be less than 4000 m/s. If you work out the equation, you find that the maximum ejecta speed is proportional only to the impact velocity, and not to the mass or radius of the impactor (although the density of the impactor is very important). Ultimately, the relationship is $$4000 \text{ m/s} = .1313v_i.$$ Thus, for a 4000 m/s ejecta, the maximum impact speed must be about 30 km/s.
How not to eject volatile gasses into space
Of the gasses you are interested in, the two lightest and therefore most likely to escape are water (molar mass 18) and ammonia (molar mass 17). Therefore, we must figure out how to keep those gasses on the planet upon impact.
First, lets look at the ejecta plume from the last problem. Using basic kinematics, a particle (of ammonia) ejected at 4000 m/s, will reach a height of about 1100 km (Don't worry! I know that this is well into space, but without orbital velocity, it is coming back down!). The time it takes to get all the way up there is about 400 seconds, and the escape velocity at this height is about 8200 m/s.
Using the calculations in the answers to this post, we can figure out how hot an ammonia particle must be at this height to escape the moon's gravity. A particle must reach about 40000 K to escape under these conditions. Ouch! Now, individual particles are able to escape because the molecular distribution of kinetic energy has some variance to it. However, given that the escape velocity at the top of the ejecta blast is still about the same as the last linked post's calculated necessary escape velocity to hold gasses over geological time (8500 m/s at Earth's distance from the Sun), I think we can assume that very little of our gaseous ejecta will hit space.
How not to change the orbit and rotation of a moon
I had some more in depth calculations here, but they are not really needed. As long as you have the technology to accelerate things to 0.1c, I assume you have sufficient space horsepower to aim your delivered payloads as you like. If that is the case, then you simply hit the moon from all directions, so the net force of the impacts is zero.
Conclusion
Find a suitable mid-size moon. Melt it. Separate the various compounds into chunks of no more than 250m radius. Throw them into your planet at impact speeds of less than 30 km/s. Very little will escape into space. Profit!
