Sicily in October, rental car, visit VIllarosa where family is from

I think it depends what you want to do on Mt Etna. If you just want to visit and perhaps walk one of the older craters at the base camp, you could likely add something else to the day. We did a “full day” that included Etna and lunch at a winery with Sicily Life. We had a car but decided we would prefer a tour particularly with wine at lunch. We were still back to our hotel in Taormina by 4ish.

We picked up a car at the train started in Ortigia. It was very simple and right off the main roads so no ZTLs to worry about. We did not visit Palermo on this trip, but it sounds like others have picked cars up closer to the city rather than returning to the airport.

One thing we did learn is that it takes longer to drive most places than expected. We found many of the autostrade were under construction.

1. rent car from airport or train station? any tips on rentals would be great!
You don't want a car in Palermo so take a taxi or bus to downtown. Rent your car from downtown near your lodging, maybe use the consolidator Auto Europe, get the full insurance, download the easypark app.
2. Day 3, do we stop to see something else besides Cefalu on our way to Caltanissetta?
Villa Romana del Casale has pretty amazing in situ mosaics.
3. We are hoping to meet some extended family in VillaRosa (researching now, my husbands grandfather was born there). Depending on what we come up with, we may spend a part of day 3 and all of day 4 in VillaRosa
4. Is Mt. Etna a full day? Can we get anything else in on day 6?
It's already too much on a 6 day trip. Skip it
5. any other suggestions?
It's a lot of running around for 6 nights. Maybe choose small hotels instead of airbnbs to support innkeepers.

I must second Chris’s suggestion about Villa Romana de Casale (near Piazza Amerina, if you are mapping a route). We have seen many Roman mosaics in out travels, but these are really next level and quite extraordinary. We actually picked up a local guide (English speaking archeology student) and she was worth the small investment. Chris is also right on skipping Aetna, especially if you have seen volcanoes elsewhere. Pretty barren and desolate the higher you go and a real time consumer.

We spent a week in Sicily this June with a rental car. First of all, know that driving a car in Sicily is not for the faint of heart. Our US road signs (stop signs, merge, speed limits) are merely suggestions to them. We picked up our car at the P airport, no problem getting out of town going west. Returning the car from the east was a different proposition as you drive through Palermo for a while maneuvering lanes? before you stumble upon the rental return lane (no indication of such on airport signs).
In the US you typically go to the counter to return the car and check in. We waited for 20 minutes for someone to show up and finally walked the aisles until we found someone. Sicily is a little dysfunctional but beautiful. We drove directly to Agrigento which is stunning and should be visited. We stayed in a perfect/modern/functional boutique hotel there :Oneira Rooms and the hosts were wonderful. Spent a night in Ragusa, had a walking tour, still amazed how they could build on the precipice. Three nights in Taormina, make sure to see the Greek Theatre, take a boat ride, and a walking or street food tour. We could have done with two nights there but the views are superb. Drove to Cefalu with the intention to stop but couldn't find any parking spot and it was overrun with tourists. Driving from T to Cefalu you will go through about 50 tunnels, no exaggeration.
Palermo was an interesting stay due to the Arabian influence. Very chaotic! We took a great walking tour to get more of the history. Sicilian olive oil and white wines are excellent, cheap, and I even learned to 'appreciate' eggplant.