It may not be strictly necessary, but you may spend a lot of time in line if you haven't bought them in advance. So if you have a good idea of when you can get there, buy them.

Just was there this past weekend. 10 minute line.
If you want to take the guided tour, I'd definitely book in advance.
You have a separate (shorter) line for entry and guaranteed not to have to wait for the first available group with space.
On Memorial weekend, you risk showing up at 10 AM and getting assigned a 3 PM tour group.

The high end mall (the Oculus) next door has a good food court and has the subway station below

If doing Statue of Liberty/Ellis Island also, its a short walk between the 2.

I am going to suggest booking an early morning tour. They have an 8:15 tour with limited space, I think 30 people. The cost is $65 but it is worth every penny. The tour is guided and since there are so few people In the museum it is a quiet experience. You will feel the difference when they start the general admission. Great way to start you day.

Yes. If you only want entry, I'd be OK with a short wait to avoid a mandatory entry time (more flexible)

If it's your first time there, I strongly advise the guided tour though!

I'd also buy in advance, and take the guided tour, if you are interested.

And a warning: Acorns generally fall in September or October, and the plaza at the memorial is FILLED with them. I found it extraordinarily disconcerting to be unexpectedly pelted by hard objects falling from above when I visited the memorial, which I though excellent in every other way.