Driving in Sicily

Can you pick up your rental upon leaving Palermo, or before your stay in the city?

I think the tourist sites like Agrigento might be the worst as far as theft from the car....probably the same in beach parking lots..and on the beach itself...

The best strategy is to pick up the car after you visit Palermo (or return it before visiting, if it's at the tail end of your trip). If you can't, leave it parked at your hotel or garage, because the city center of Palermo is largely forbidden to non residents' cars, so it's not difficult to drive if you don't mind a bunch of tickets for unlawful entry in the restricted zone.

I've left the luggage in my car while visiting the Valley of the Temples. Nothing happened, but like everywhere else in the world, it's a risk you are taking. Statistically it is less likely that my car will be burglarized in Agrigento than in Oakland, California, where every few years I've had to replace the smashed window, but it can happen anywhere, so at least take the most important items with you and lock your suitcases to the trunk interior using a cable lock (like the ones used for bikes). I usually do so in Italy, where I can't avoid, but it's a risk, especially in large cities.

I can tell you that in the 3 decades I lived in Italy, my car (or my parents' car before adult age) was burglarized only twice, once in Florence (my city) and once in Riomaggiore (Cinque Terre). Since those years, although I have a car in Italy every time I go (once or twice a year), I was never a victim of car burglary again in Italy, while here in California I can't even count anymore, even if all I have is change in the ash tray.

I had no issues driving around Sicily, but we only had luggage in the vehicle when we stopped at Villa Romana del Casale, Selinunte, and the Marsala and Trapani salt farms.

Take a few precautions to reduce the chances of becoming a victim.

Leave nothing in sight (maps, coins, cables, bags, etc.)
Have everything in the trunk before arriving at the parking lot so you don’t have to open it where prying eyes can see what’s in it.
Don’t park in isolated places.
Park in a location where people regularly walk by.
If possible, back into the spot where there’s a tree or wall behind the vehicle, and back up close enough to the tree or wall so a person cannot fit in between and the truck/hatchback cannot be opened.

Palermo is a pain to drive in and I didn’t even drive in the main part of it. Rather than drive in Palermo we stayed in Monreale and took the bus into the city.

Driving in central Palermo is not "fun", but it's not difficult or hair-raising really. You just have to be really attentive and not get stressed about your car being much, much closer to other vehicles than is typical in the U.S. Drivers nudge into the flow and weave out "aggressively" but it's a bit of a ballet. Drivers are gruffly "courteous" in this regard and let you do your thing as long as you don't dawdle. It's not everyone's cup of tea and it took a bit of time to get used to, but by the time I returned to Palermo, I barely noticed it.

But from your description, it sounds like you're planning on renting your car at the airport, driving to Palermo and parking it? I absolutely would not do that. You don't need or want a car during your Palermo stay. It's gonna be an expensive hassle and a source of worry. There are plenty of rental agency offices right near your hotel. Just pick up your car there the morning you leave Palermo. And there is no reason to waste time and money backtracking to the airport to rent from there.

I can't speak to security/theft. I have happily never been a victim. We parked in some pretty remote spots but we never left anything in the car beyond a bottle of water; nothing of value and even nothing like a brochure or guidebook to mark us as a tourist.

We drove into Palermo last year, and left the car during our stay in the garage arranged by our Airbnb @€20 a day. You can buy a ZTL pass through the Palermobilita app -€5 a day. You only need to have a pass for the days you actually use the car in the ZTL zone - so don’t need one if your car stays in the garage - and you can buy pass up to midnight on the days you need one., arrival and departure days in our case.