Hi and welcome to the forum.
There are a few videos on youtube; start by watching this one.
Unfortunately some of the roof parts would appear to be fragile, and cheaply made - but they are not cheap to buy, if you can even get them at all. A Fiat franchised dealer will likely fix this by replacing the roof complete; expect to pay at least $7000 - $8000.
In the UK, there is an
aftermarket company which will supply and fit a new soft top for £4250 - that's a shade under $6000.
If it were my car, I'd be searching the web to find out how the mechanism works and what has actually broken, then I'd trawl the 'net and the breakers to try to find whatever parts I needed.
Please keep us informed about how you get on with this - it could help someone else with a similar issue.
Others have said the same thing in the past; most soft top restorers in the US will be completely out of their depth when working on a car like this. You don't want to be paying them to learn how to fix it, using your car as a guinea pig, so the first question to ask is "
how many other 500C roof repairs have you done?"
Interestingly, though there are quite a few 500C owners on the forum, we don't see that many posts from folks having problems with them, so you may just have been unlucky.