Yes, you can use the RS walking tour. If you'd like more, there are also group or private walking tours. Or you can simply use a city map and do your own walking tour. It's up to you.
All the main sites, including the Acropolis, are in the same area, which is largely pedestrianized.
The Parthenon is one of the monuments on the Acropolis Hill. You must therefore purchase a ticket for the Acropolis. It can be purchased in advance on the official website by specifying a date and time slot.
https://hhticket.gr/tap_b2c_new/english/tap.exe?PM=P1P®ion=000000007
When the hotel has its own website, people book accommodations directly on the hotel's website. If you want to book through Priceline or booking.com, or whatever, it's up to you.
With only 4 days, you can't visit Athens and go to Delphi, to the Meteora, and to the Peloponnese. You would need at least 12 days, provided you optimize the trip as much as possible and rush from one place to another with a rental car.
The closest place is Delphi; you'll need a full day to get there, visit it, and return to Athens.
So you'll have to make choices.
All these generalities are perfectly detailed in any good travel guide. I think you should start by reading one (or two) of them.