I am sure that there are members from the NYC area, both past and present, who can offer some very good advice on what you plan to do, but if you will be staying in Brooklyn and in the area for only three days, you may want to check out some of the Italian food stores in Little Italy, just outside Chinatown and on the way from Brooklyn into lower Manhattan. The three Italian food stores I frequent while in that area are the Alleva Dairy (188 Grand, at Mulberry), Italian Food Center (186 Grand, at Mulberry), and DiPaolo Fine Foods (200 Grand). As you can see, the three stores are all on Grande and close to each other. In fact, Alleva and Italian Food Center are on opposite sides of Mulberry. Alleva is reputedly the oldest cheese store in the country. It specialized mainly in cheeses but it also has dry sausages (includiing pepperoni), cold cuts, some olive oils, olives, etc. The Italian Food Center sells the same things but more, especially in the non-cheese area. It also sells some mean freshly-made sandwiches. DiPaolo sells much the same products as the others. It seemed to me that the people who work behind the counter there were more knowledgeable than the others about Italian foods in general and their products in particular. Any one of these places is great to buy some Parmigiano-Reggiano cheese to bring back home with you. The PM will be super fresh and reasonably priced compared with most other places back home. You might also go across the street from Alleva to Ferrara's for some really good Italian pastries, to eat some there with a good cappuccino and to bring some cookies back home with you (which is what I always do).
You will find fresh mozzarella cheese (fior di latte) at all of Italian markets mentioned above and my recollection is that they all offer buffalo mozarella cheese. You are unlikely to find much in the way of 00 flours at any of them, but if memory serves me correct, I think I did see some Bel Aria 00 at one of them. The Italian Food Center and Paolo carry canned tomatoes, including some San Marzanos, but the last time I was there the pickings were slim. I'm sure that there are better places to get the San Marzanos if that is what you are interested in. I just don't know where they are without taking you too far away from Brooklyn.
The original Ray's is said to be the one at Prince and Mott, at 27 Prince. Lombardi's is at 32 Spring. They are both a short distance by foot from the Italian food markets mentioned above.
Of the pizza places you plan to visit, I believe that DiFara's is the only one to sell slices. I am not even sure that Ray's at Prince and Mott does, but I may be wrong on this. When I went to Lombardi's, I made a point to get there just as they were opening the doors, just to be certain that I would be seated. The place is very popular with tourists, and they start to line up outside the doors once it opens. I was at DiFara's just after lunch and had to wait a while to get the pizza, but I was more interested in watching the master Dom DeMarco at work.
Depending on which days you will be in Brooklyn, you may want to check to see that the places you want to visit will actually be open.