Yes, you can pay dining tabs with a Disney gift card at most restaurants at WDW.
Notable exceptions include, but are not limited to, most of the table-service restaurants at Downtown Disney.
A good rule of thumb is, if it's on the list of places that take the
DDP, then it's going to also take Disney gift cards. There are actually a few places that don't do DDP which might take the gift cards, but the DDP list is a good starting place.
Not sure about adding value to cards once they are purchased, but there's nothing stopping you from buying another $25, $50, or $100 card periodically and using them at WDW (one after the other until they're used up).
As for non-dining use, they are valid in most places in the parks (some places in Epcot don't take them, for example) for merchandise, and they are valid at the resorts for shops, dining, and for paying on the charged balance on your room key. At Downtown Disney they are valid in some places, but mostly on the Marketplace side.