The player controls the whole side.
Fabbers save up a $ amount each turn.
If you've got $4000 saved for example, you can use the (B)uild command on it and you'll get a list of all the designs you've made.
Select which design, what direction you want it to start out facing, and how many you want to build.
The cost of the ships are deducted from your Fabber's savings.
You don't have to upload the ship at all. The design will be included in your PLR file as part of the orders.
If you have a drydock or spacedock, you can repair your fighters by docking them, building some loose components and then docking the components next to your fighter's hull where it will stick.
For bigger ships, you can design a "ship" composed of a component, some hull and a string of explosive bolts in the right shape.
If you've shaped it right, the ship can grab the bolts with a docking clamp, and that will cause the component to slap into place on your ship.
Note: When docking, any components that were there already get first dibs on staying put. If there are any collisions between the existing components and the ship you are docking, then the offending components will be knocked free and reappear as loose debris.
This lets you spot weld new components on for repairs and upgrades as you go.
Scavenging parts from destroyed enemies is great for this. Scrapping and rebuilding incurs a 50% value penalty unless you're using a recycler, but if you can reuse a part from an enemy, its better than free
If the enemy is throwing missiles at you, shoot them down and then grab the remains with a clamp-drone. Shield generators and capacitors are great value per size, but you can also usually find a bit of hull to grab with lots of other stuff stuck to it.
Regarding missiles, the warhead range is 5, but there is a 1/R damage falloff. Objects in the same hex get hit from a random angle, so you will probably want to have the warhead detonate one hex away to ensure you hit the weakest side of the target.