Maybe someone will be able to find the videos of both times. It is my recollection that the jury had been dismissed both times before the judge asked Zimmerman if he wanted to testify. If I recall many years back when I was on a jury the defense didn't testify and I am pretty sure we never heard the Judge ask if they wanted to.
I think it would not be appropriate to ask in front of the Jury because just him answering to that question by the judge could have an influence on the jury. You would then see his manner etc as to how he answered.
You are correct the jury was NOT present for either time the judge asked GZ about taking the stand
Believes the jury has been listening carefully - intuitively
The jury was not there either time. West was objecting because “the question” was being asked before they were finished with their presentation. She was pushing. Oh yeah, this is schedule oriented.