Look at the reservation calendar to see how far out there is availability. Then you will have your answer

We booked about a month in advance in March 2021. I would suspect a shorter notice is possible now, but worth going ahead and booking as soon as you know your dates.

If you are staying a day or a few, a few months. If you want to stay weeks, better to plan at least 6 months out when you can make that kind of plan.

It depends on the month. May/Oct u can probably get same day. Oct-May tourist season is on. So it’s harder to get reservations so 3-6 months in advance. Or just wait and check daily for cancellations.

It really depends on what time of year you want or weekend vs. weekday. We have had good luck booking a month or two in advance. You can quite easily cancel if you change your mind.