You haven't said when you want to go to Greece.
we would like to visit Santorini, Paros, Milos, Lefkada, and Kefalonia
Santorini, Paros and Milos are in the Cyclades Islands. Lefkada and Kefalonia are in the Ionian Islands. Island hopping is not possible between these two island groups.
Anyway, visiting 5 islands in 2 weeks is too much, sometimes even impossible. 3 islands is the maximum if you don't want to spend your time on transfers. Moving from one island to another takes most of the day.
You can check ferry schedules and prices by consulting ferryhopper:
https://www.ferryhopper.com/en/#/
And don't forget that you will have to return to Athens at least a day or two before taking your return flight
From the twenty islands in the Cyclades you have chosen 3 of the most touristy islands. I don't know if this is intentional or if it's a random choice. Why not the other 17 islands?
https://www.visitgreece.gr/islands/cyclades/
Would it be better to fly to and from Athens and take all the ferries
to those islands?
After a long flight, if your first island has an airport it is advisable to take a flight to that island from Athens as soon as you arrive.
Then you can travel from one island to another depending on the ferry lines and schedule, but above all if there are ferries for the journey you want to make.
We are interested in the nice blue crystal beach with local cuisine
and outdoor activities.
They are practically everywhere on all 200 Greek islands.
Which island do I really need a car? Which car company allows island
hopping?
The need for a car depends on what you want to do and see, where your accommodation is located on the island, how long you stay there, and on the island's bus network.
There is no need to rent a car and take it on the ferries. You'll pay extra for insurance, pay the ferry ticket for the car (and not all ferries accept vehicles) and that car will be of no use to you when you're on the ferry. If you have a mechanical or other problem with the car you wont have any assistance.
There are local rental companies on all the islands. It's much simpler and cheaper