Yes, if you use the Disney Visa to make any payments on your trip you will earn reward points for the amount(s) you charge. You also get 0% no-interest for 6 months to pay off vacation packages (the financing option is not available for room-only or ticket-only purchases or onsite purchases - but you do earn rewards on those).
You earn 1% rewards on all purchases, and another 1% (so total 2% rewards) on gas, grocery store, restaurant and Disney purchases. Those rewards points are equivalent to dollars. When ready to use them (must have minimum $20 rewards available), you'll transfer the rewards to a Reward Redemption Card which can be used for pretty much anything Disney -- parks, resorts, tickets, souvenirs,
Disney Store (online or brick-and-mortar),
DCL, etc. Yes, you can purchase Disney gift cards from the Disney Store with your rewards.
The Premier card also allows you to use the rewards to pay for airfare; that is not an option with the regular no-fee card.
We put most purchases and some bills on our Disney Visa. The annual fee is covered in a month or two, the rest is our vacation savings. It works well for our needs. There are other cards that may work better for other families depending on spending habits and such.