You cannot make custom ships, however, you can apply custom images to existing ships. To do so, you need a 400x300 image and matching 100x100 image with a Combine frame, and then go to your CP Exchange (Click the number of CPs next to the CP under General, then click CP Exchange), and upload your new custom images. After it has been accepted, the CPs will be deducted, and you will need to apply it to the specific ship.
Datacards are acquired from the faction that holds them. In the Rules page for each item, it lists all factions that hold the Datacard. You must contact the representative for that faction and give him/her the ID for your factory or shipyard and transfer the agreed upon amount of credits, and they will assign the Datacard to that Factory or Shipyard.