[Taera]

Bases are static, hence you would need a SpaceYard ship. For this you would need at least Cruiser size.

If you build a Base Space Yard it can construct ships and units, but only at about 50% rate.

To deploy sattelites/mines you would need a ship with appropiate launching component (sattelite bay/mine bay). Design a ship with this component, construct it. Once you load appropiate cargo you could launch them, limited with the launch-per-game-turn stat, which can be seen from component's description.