Will my US Handicap playcard work in Italy & free parking?
There is an agreement to recognize US placards in Europe (Specifically the EU), so yes.
However, if the spot is in pay parking, you still pay, and a placard does not likely forgive you in ZTLs.
Can an African or SouthAmerican come to your town with a placard issued in their home country and park in a handicapped stall and for free?
when I travel around Europe with my wife's Blue Badge (and her of course), I rely on the country by country current information from the official EU website. http://www.disabledmotorists.eu/en/world_map/europe/europe.htm
For Italy it is http://www.disabledmotorists.eu/en/world_map/europe/italy.htm
I suggest that you read the page carefully. It is probably the least welcoming to non-Europeans I have seen.
Only in some parts of the country is a non-European placard accepted, and in many cases it is not free, just not time limited.
Please check carefully. Many countries in the EU are more welcoming to a non-European placard.