Thieves don't usually break into cars if nothing is visible - that's the key , nothing visible.
Both tourists and locals have their cars broken into when items are visible.
Local friends of ours had their car broken into ( by smashing the window) and items stolen.
Everytime I rented a car the Via Verde transponder belonged to the rental agency, they charged me for the tolls after returning the car.
They usually charge a rental fee for the transponder additional to the toll fees.
If you're absolutely sure you're not driving on a toll road you won't need the transponder.
That means driving on the side roads.
I always buy the CDW from the rental agency for the peace of mind and to avoid the hassles if it's necessary to make a claim.
This is based on my experience:
The rental contract is between you and the rental agency not the Credit card company.
You are the renter and the driver, if there's a damage claim the rental agency will request payment from you , afterwards you will have to request to be reimbursed by the CC.
Contact both the rental agency and CC if that's their procedure or if it's different.