Ah, there is a big difference between a satellite and a MOON
1) Does your ship have a strategy of "Don't get Hurt", leading it to run away?
Go to the design window, and click the Stats/Strategy toggle button to see.
If you ship has no guns on it, it will also usually run away and hide. (Unless orders are to ram, drop troops, etc)
2) If there is already a colony on the moon, send your colony ship somewhere else and drop Troops (Tanks, jets, etc) on the enemy-held moon. You can get troops by researching Construction, then troops. Build some, load them on a cargo ship, and give it orders to "Capture Planet", then attack.
Alternatively, you can nuke the planet to glass with a warship, and then recolonize the newly-uninhabited world.
3) Atmosphere converters are found in the "Planet Utilization" tech area, at about level 7.
You may need to research "Planetary Engineering" first.
Once that is done, you can build a facility which will change the atmosphere to whatever the population breathes. After 2-3 years of invisible work the facility will be done and the atmosphere will change.