Not US English, but maybe something useful to you.
>>Hi, I'm looking for the exact term in US english for an application which is not corresponding to any job adverts. I've read "speculative application", is that correct ?
Do you wnat an official, formal term, or simply be understood and seem native?
"speculative application" - seems fine.
Inmy English, I don't think I have a special term for this. There likely is in formal HR-speak.
>>Moreover, I was wondering how can I call my résumé section dealing with association activity, and if you're used to seeing it in the résumés in the USA.
I was wondering what can I call ... <-- what can I call something, what do I call something ..
What is "association activity"?
Do you mean, such as professional organisations, linked-in, viadeo?
affiliation? memberships? professional memberships? professional affiliation?
Sometimes, here, this appears as associations, memberships, honours, awards
I suspect that CV style varies more regionally than nationally. There will be overall trends, but short, long, detail, these things change, check the most current info you can.