Is it permissible to testify to what was said in secret during an informal session aimed at resolving a dispute between two parties, or is what was said considered a trust of the gathering that may not be divulged?

If the matter you know pertains to the rights of human beings, then it is not permissible for you to bear witness unless you are asked to. It is legislated to inform the right-holder of what you know if they are not aware of it, and your testimony is not considered a disclosure of a secret. However, if the testimony pertains to the rights of Allah, then you are obligated to render it for Allah the Almighty without anyone asking you.