1- I gave the keys to Sarah.
2- I gave Sarah the keys.
I've already know the grammatical role of "keys" and it's object. What about the "Sarah"? Is it the second object or what? (In both examples)
I need the word order & exact structure for further analysis could you help me ?
OP's example #2 is a ditransitive usage - it's got two objects with no prepositions. The keys (the thing given) are the direct object, and Sarah (the receiver) is the indirect object.
Note that with some verb + object combinations, a ditransitive verb becomes monotransitive by removing the indirect object. Hence ditransitive He bought me a coffee becomes monotransitive He bought a coffee (note that He bought me isn't valid in any normal context). Also note that to give almost always requires both objects (the thing given and who it's given to), but it's not normally (or at least not necessarily) still called a "ditransitive" usage if there's a preposition, as per OP's example #1.
Many verbs of giving or showing are ditransitive in English, and allow these two different argument structures:
I gave the keys to Sarah. <=> I gave Sarah the keys.
Sarah showed the book to me. <=> Sarah showed me the book.
Tom offered a cake to them. <=> Tom offered them a cake.
In each case the meaning is the same, and you can see from the to that the recipient is semantically an indirect object, and the thing given, shown, or offered is a direct object.
As long as both are present, you can put the indirect object before the direct, without a preposition.
Other verbs which can be used in this way are promise, present (in the sense of "give in a ceremonial way"), and sell.
This is also possible with some other verbs with a "benefactive" object, using the preposition "for":
I baked a cake for Sally. <=> I baked Sally a cake.
He built a house for us <=> He built us a house.
Will you buy some oranges for me? <=> Will you buy me some oranges?
The benefactive (the person you're done the action for) isn't part of the meaning, so it isn't required (He built a house. I baked a cake) but if you expressed it, you can use this ditransitive construction.
But you can't do this with every verb
I washed the windows for her. But not *I washed her the windows.
I think the restriction is that the beneficiary must end up with something they didn't have before.
