You should, by all means, call the court with your questions. The usual practice is to indicate a phone number for the court bailiff, who handles the scheduling and "management" of the jury pool.

Many courts now do permit almost anything in the pool waiting areas, but security for things you must leave there if actually called into the court is extremely variable. Most will tell you that "the room will be secured" while you're away, but their idea of "secure" may differ from yours, and there invariably will be other prospective jurors there when you aren't, so ...

A few courts do provide "lockers" where you can deposit personal things that you need to leave unattended (but that may not "lock" unless you provide a padlock?). NYC may be a big enough system to have this rather progressive feature, but I would want authoritative confirmation that my stuff would be safe. Courts are, after all, populated with, and accessible to, quite a few criminals, some of whom may have been not yet disbarred caught.

For any case that might receive local news publicity, newspapers - and probably radios/TVs likely would be off limits to those in the jury pool, since opinionating often peaks at the time of jury selection.

John