Q. Do you think a producer can damage you and your spec script talking about it to people (e.g. other producers, tv and funding ceo and so on) before having actually bought it himself?
I don't know why a producer would tell other producers about your script unless it wasn't for him. Why would he? He doesn't control it. If I were a producer, and I was interested in a script, I wouldn't do anything about it until I'd optioned it.
The exception would be producers who have a relationship with a studio, who would take a script to their studio to get money to buy it. I suppose if they have a financier, same goes.
You could be dealing with an "emerging" producer or someone who doesn't have the resources to option your script. They might take your script to bigger producers they know to get money to option it. But they would probably not do that without at least a shopping agreement that attaches them to the project in the event they get it set up somewhere.