Just to confirm,
Dámelo is not a contraction and actually it is a grammatical structure that works as an order or like in the case of
Me lo dá? as a polite request.
The tone changes since the way you request is different and probably you will choose one of them depending on who you are addressing (
Dámelo is informal and direct,
me lo dá? is formal and polite). You may find this review of Spanish grammatical structures useful.
On the other hand, contractions are shortened versions of the written and spoken forms of a word or a group of words, and are created by omitting internal letters. The typical examples are:
A + el = al
De + el = del
There are other examples which are not so common(as far as I know) in Latin America such as:
Donde + quiera = doquier
De + esto = desto
I hope this helps!