Am I allowed to testify in court with my wife's sister that her husband used to beat and verbally abuse her, based on what she used to tell me, even though I did not see or hear that myself?

As long as you have not personally seen or heard the husband striking and insulting his wife, it is not permissible for you to testify against him based on the wife's report. Testimony must be based on knowledge. The Messenger of Allah, peace and blessings be upon him, said: "Do not bear witness except to that which is as clear to you as the light of this sun." The basis of knowledge upon which testimony is given is sight and hearing. As for what is observed through sight, these are actions, such as adultery, drinking alcohol, and all other actions.