The number of cost included restaurants varies depending on the ship you're sailing.
The table sizes also vary depending on the restaurant... though tables of 2 to 8 are pretty common.
I would reconsider the decision to not eat in the surcharge restaurants. Add about $60 per person to the cost of your cruise fare. If it's still a good deal, enjoy a few nights in the surcharge specialty restaurants, and take full advantage of NCL's freestyle experience.
As far as dining with others, you'll have to make friends on the ship, and make arrangements to dine together, as the cruise line normally does not just match people for tables as they come in.