Float chargers are designed to maintain a fully charged battery and are a good idea. If concerned about leaving plugged in 24/7, just hook the charger to a simple timer that will run the charger for a couple hours each day. Newer cars do have a lot of small electrical drain items that will deplete a battery over time. Either disconnecting or using a float charger are good ideas.
Correct that oil pump is only working when engine is running. It is mechanically linked to engine rotation. What may be confusing is that all new fuel injected cars have an electric fuel pump that needs to build pressure before starting. So for a vehicle that has sat for longer period, turn ignition to on position and wait 5 seconds or so for it to pressurize before starting. The fuel pump will run initially for 5-10 seconds when the ignition is turned on by the computer in the car, and then turn off it is not started. It won't keep the fuel pump running if the car is not started.
