She kept asking him if he wanted to testify over the objections of Zimmerman’s attorney. It’s not the judge’s place to ask such a question. It is up to the defense whether the defendant takes the stand, and no one else.
We know that "vengeance for Trayvon" types tried to get themselves included in the jury...we just don't know if any managed to elude O'Mara's vigilance. One or two diehard "death to Zimmerman" types could try to badger the other jurors into agreeing to find him guilty of a lesser charge to avoid a hung jury.
Yes it is the judge's place to ask such a question, and the question is actually posed in order to protect the defendant (and, of course, to protect the judge from being overturned on appeal). Per a Supreme Court decision from the 70's (I believe, can't remember the case off the top of my head), there is a Constitutionally-protected right to testify. While a Defendant may of course waive that right (under the corresponding 5th Amendment right against self-incrimination), under Florida law, "[t]he record must support a finding that such a waiver was knowingly, voluntarily, and intelligently made." Reynolds v. State, 99 So. 3d 459 (Fl. 2012).
Indeed, contrary to your assertion that it is improper for a judge to ask, the Florida Supreme Court has written that "[a]lthough a trial court does not have an affirmative duty to make a record inquiry concerning a defendant's waiver of the right to testify, it would be advisable for the trial court to make a record inquiry as to whether the defendant understands he has a right to testify." Id.
She was totally bizarre and out of line. I have never seen a judge try to go around an attorney and ask the defendant something like that directly. Unbelievable!!!