Hello.

I want to ask. Is it possible to fly in some American Airline with JAA licences or only need conversion?

No -
Flying for a US air carrier requires a FAA pilot certificate.
A minimum of CPL/IR/Multiengine level certificate is required for F/O position.
There is "no conversion" of JAA licences for airline flying.
Approved FAA training and tests are required for JAA licence holders.
xxx
:ok:
Happy contrails