When peri-operative jobs are posted, by and large they refer to Pre-Op and PACU positions. Some smaller surgery centers though may require the ability to scrub in as well depending on the size and demands. But in those cases, it's rare that you are doing all three tasks at once. Given your ICU experience, that is the backbone of what most consider adequate to do well in PACU. But it isn't the be-all end-all as I spent the better part of the past 7 years excelling in pre-op/pacu fresh out of nursing school
In regards for prepping you to be an FNP, I can categorically say that it will not. FNP is certainly focused on broader disease knowledge/management where PACU's primary focus is airway stabilization, pain management, and safely moving the patient on to the next point of care in a timely fashion. As someone who just passed his FNP boards, my choice in Perioperative services and pain management was probably among the least helpful paths I could have taken. Thankfully I had a strong study group to help pull me through school and pass my boards.
Every facility is different and has it's own issues in regards to your interview questions. Every PACU I have worked has had a 2 patients to 1 nurse ratio for non-critical patients and a 1-1 for what they consider "ICU level" patients. Though this can vary greatly. Call is important in any OR operation, but many places have a substantial staff pool to accommodate it. I think most places I worked 1 weekend day of call a month to 8 weeks.
Unit cohesiveness is an important thing that many people don't think to ask about. Periop is a team environment. While we are easily focused on our patients, you need a keen awareness of the OR schedule, the patient rotation, and how holding onto your patients impacts your fellow RNs. Knowing and accepting early on that this patient may not be "fixed" before they leave your care is an important thing to learn early on as their time in PACU should be for a minimal period. Another thing to ask about is how the patient's come out from surgery. Most places I've worked have some form of grid and assignment order. OR calls to a charge, charge gives an assignment, RN is notified, patient comes out. This flow can make or break a work environment. I worked with an RN once who was happy to be leaving our facility which she often drove up to 2 hours to when traffic was heavy to a PACU 10 min from her home. She was back less than a month later because their "system" involved the OR arriving with a patient and going into the first slot they saw open. At an equally busy facility, she said she'd gladly suck up a 2 hour commute. So absolutely verify they have a system in place.