1.
It doesn't sound odd, but it does sound like they paid her to kill the child. You might want to make it clear that they didn't do that (or if they did, that's one evil company)
2.
I'd agree with Peachey that a judge presides over a case. But US usage will let you say "the judge on the case" in casual speech.
3.
"Is," "is," and "think" are indicative mood. "pay" and "have" (not pays and has) are subjunctive mood.