Translation:I want a sandwich without egg please.
"Graag" is closer in meaing to "gladly", I think, which is why "Ik wil graag" translates as "I would like" (literally: "I want gladly") and "Ik lees graag" translates as "I like to read" (literally: "I read gladly").
If someone offers you a drink (water, beer, wine, etc.), you can say "Ja, graag" which is like saying "Yes, gladly" (but probably best translated as "Yes, please" in English).
For ordering, I don't think I've heard anyone say "graag" at the end. Like PaulineStinson says below, it would be "Ik wil graag..." You can also order by saying "Mag ik een boterham, alsjeblieft." "Hebben" is usually left off because it's implied by the auxiliary/modal verb "mogen".
Also, "graag gedaan" for "you're welcome" can be thought of literally as "gladly done".
They have a different meaning, u is a polite form and jij an informal form that you normally wouldn't use for people you don't know. Just like Sie and Du in German, vous and tu in French, usted and tú in Spanish, et cetera. So, when ordering in a restaurant, use alstublieft, when your dad wants to know what you want for breakfast, use alsjeblieft.