US based attorney here. Please note the below are general statements in response to your question (and a few others I've seen here on the board), and there are variations from court to court:
--Megan has been trying to get this case tossed at an early stage of the litigation before discovery. In US courts, that is a very difficult thing to do before discovery takes place. So I am not surprised this is going to discovery. That is not reflection on the merits of the case at all.
--discovery consists of written interrogatories/request for production/request for admission AND oral deposition under oath.
--Written interrogatories/Requests for Production/Requests for Admission--you've seen what Sam has asked for floating around the internet. That does not mean she will get what she asked for. Any reasonably competent attorney will object to many of these requests as too broad, not relevant, or unlikely to lead to the discovery of admissible evidence. Meghan's side will probably win some of those objections because the questions I've seen are very broad and not necessarily related to the issue at hand (whether Meghan defamed Sam). They'll fight about those answers, and we may never see rulings on them, or the answers.
--oral depositions are usually a question and answer session on video and under oath. Think of it as an "interview" with a real reporter who asks hard questions with follow up questions and under oath. So to answer your question--yes, this is a "live grilling." They can prep ahead of time for what they think will be asked, but they cannot turn to their attorney with a question pending and ask how to respond. So no rehearsal with a friendly interviewer, and no chance to ask for lifeline. The attorney for Meghan/Harry has a limited basis to be able to object during the deposition and tell the witness not to answer. This why Meghan's team fought so hard for it not to get to this stage. Please note that Sam also will be questioned under oath by Meghan's attorneys.
--Not everything that happens in discovery is posted on the docket. Just because you don't see answers to interrogatories or depositions, that doesn't mean they haven't taken place. You may never see their depositions. You may never see her answers to interrogatories.
--to clear up something I see here all the time--Sam is not asking for $75,000. She is asking for an award "in excess of $75,000. This is standard pleading language that gets you into the right court system. If she wins an award from a jury, it could be more or less.
--can this case still get thrown out? Yes. After discovery, there will be another round of motion practice, including summary judgment motions. The standard for summary judgment is high in US courts, but it is possible the case can get tossed later on with a new round of motion practice.
--will the trial be televised? Assuming it gets to the trial stage, this is very Judge dependent. Most Judges, especially Federal Court judges, do not like their courtrooms to be a circus. Do not count on it.
--why is Meghan referred to or not referred to in the papers as the Duchess of Sussex? The Court will not give a shit about her titles. Meghan makes her attorney drop it in papers they file, which is just breathtakingly arrogant If this goes to trial, there will be motion practice to keep her title from being used in front of a jury because it is not relevant and highly prejudicial.
--can they settle the case? Meghan is the one being sued. She decides if she wants to make an offer and Sam would decide if she wants to accept it. Meghan can offer a settlement package and Sam says no.