2012 Fiat 500c Lounge Tan Roof Grease spots

What exactly are you attempting to get at? The only greasy parts of the convertible top are the guide rails (on both sides) and the guides (the part of them that go into the rails). Just open up the top all the way and see if there is any excessive grease sticking out from the rails. While the top is only partially open, take a look at the top guides (in between the folded fabric) to see if there is any excessive grease anywhere. Chances are - you won't find any, and the car was probably stained with something else, from the outside. You can remove most stains with the proper chemicals. Just do not use any hard brushes, or chemicals that might damage the fabric.

Also, if I were you, and was using a cheap car to get around, the spots on the top would be the last thing on my list. When was the last time the car had the engine oil changed? How about brake fluid? Did you do the applicable mileage inspection, as specified in the owner's manual? Does your spare tire has any air in it?

No problem. But please, make sure that you familiarize yourself with the necessary maintenance, etc. Owner's manual is a good start. If you do not have one, they are available on the net: https://www.dezosmanuals.com/wp-content/uploads/2021/07/2012-Fiat-500.pdf Having a pretty car is, of course, nice, but it would not be very useful if the wheel falls off while you are driving (that is actually more common than people think)
Make sure that: engine oil, transmission oil, brake fluid, coolant are fresh and are not leaking.
Make sure that the serpentine belt is good. Check if the timing belt is due.
Check brake pads and rotors, check the tires for proper wear.
Of course, you also need the lights, wipers, working and properly adjusted.

Also, have someone check the CV boots and tie rods.
The rest of it is a bit more complicated, but usually lasts longer unless the car has seen excessive wear or has been in an accident.

Very good. Still waiting for those pictures

Looks great!
Nice color, too.