1. Most of the native speakers I know would write, "The plan was not approved and therefore abandoned." In official proceedings, there is a difference between "the plan was not approved" and "the plan was disapproved". 2. I think the correct and unambiguous way to write this is either (a) The attorney's cross-examination undermined the credibility of the witness; or (b) The attorney's cross-examination broke the witness. The two options mean different things. From your original sentence, it is not clear what you intended to say.

1. There's nothing wrong with this sentence, although you could alternatively say 'led to the experiment being abandoned'. 2. Sounds fine to me.