Do you need reservations for all restaurants other than main dining or just the pay restaurants, and if you do, do you really need to book the first day of the cruise?

It is not necessary to make reservations. However; if you want to eat at peak times, you might want to make reservations in the morning of that day.

Just having sailed on the Jewel, I would strongly suggest you immediately make reservations for any restaurant you're interested in unless you like to dine at 10pm! If the ship is not at capacity, it might be better, but many on our ship never got in to any of the restaurants pay or otherwise!

Do the main dining restaurants take reservations, or just the specialty dining?

The main restaurant does not take reservations, but on the Dawn, there was never a wait more than 5 minutes at the Venetian (except for the midnight chocolate buffet). The Garden Cafe was often crowded, to capacity at times, but most of the time there was no problem finding a table.

For those restaurants that take reservations, I recommend you select restaurants that do not charge an extra fee. See my review at http://www.cruisereviews.com/NorwegianCruiseLine/NorwegianDawn71.htm

The main restaurants will, but you have to arrange it with the head ma-it'd. The reservations desk in the atrium or lobby will not do it.
If you have a very large party, you find a table much faster if you reserve a table in advance at the main restaurants.

We're just a party of 2, early 20's and we eat later than most. I just wanted to make sure that we wouldn't have to wait until 10 to eat.
I've heard that if you make reservations for the sushi restaurant that it does not include any of the other asian restaurants. I love sushi, but my husband doesn't so im not really sure what to do.