Colonies do not shoot. Their only defenses are ships in orbit.
You cannot build attack or defense modules on a colony.
Orbital Fleet Manager allows orbiting ships to fight as a fleet, without it they are attacked one at a time.
Planetary Defense gives a 25% increase to your planets defenses against invasion by troop transports. It will make your planet more likely to come out on top in the event of an invasion. Remember warships cannot hurt your colonies, only transports and sporeships can. Hope this helps  

And remember, a colony can only be invaded by a troopship or sporeship if it is undefended. If you have ships in orbit, your enemy must destroy them first in order to land troops or deploy spore weapons. And as said, if you have an orbital fleet manager on the planet, it will allow your ships in orbit to act as a fleet, instead of being attacked one at a time, which can come in handy if a fleet of enemy ships is attacking.

There are several super projects that can help your ships in orbit. The 'omega defense' improvement (you can only make one in a game) doubles the hit points of ships in orbit, and the 'hyperion fleet defense' improvement (also, one per game) allows all of the ships in orbit of that world to act as a fleet, regardless of your logistics ability.

And like Tral said, the 'planetary defense' improvement adds 25% to your soldiering ability on the planet, making your citizens more resistant to invasion, should your orbiting defense ships be destroyed and your colony invaded. You can build as many 'planetary defense' improvements on a world as you wish, their effect is cumulative.

1. That's probably an orbiting vessel defending against attackers. Colonies can't fight combat ships.

2. Constructors can't add modules to a colony directly. They can have an influence by building modules on nearby starbases to give orbiting ships bonuses or the colony itself a production/research bonus.

3. Orbital defence lets your orbiting ships act as a fleet with the maximum size depending on logistics. The use of building it is situational. By building it, a group of vessels is thrown in combat. Some people don't build this with the logic that, when the attacker blasts the ships one at a time, they have to spend more turns clearing the defenses. A fleet with say four moves would need one turn to destroy a fleet of five tiny ships but it will take two turns if they don't band together.

Planetary defence gives a 25% combat boost for your troopers. In essence, I think it is the same as having 25% more soldiers. It's usefulness depends on your morale situation. If you have a high morale, you may want to consider putting a farm there instead. It will provide a bigger bonus on basic colonies (6 billion basic population and 3+ from the farm against 1,5 virtual soldiers from the planetary defence). On top of the, farms provide tax-payers.
If morale is a problem in that you can't raise it above nine billion, planetary defences will be interesting.