About Registering and Shipping

I want to have to proccess for registering and shipping, i mean,
first i want the customer to input his name, adress, etc... and the i want to create another form for the person he or she is sending the gift, i mean modify the fields when you choose the shipping adress is not the same than billing adress and the fields in billing adress should be different from shippig adress.
Can it be done?

Yes. You should create custom fields of the table "order" via the menu Display>Custom fields for that. That way, they will be displayed on the checkout ( you can have them on a specific step if you want by changing the checkout workflow in the configuration ) and the information will be attached to the order, not to the address.

and is it possible to choose what custom fields appears in what part of the checkout process?

There is only one fields view on the checkout and it will display all the custom order fields. You can move it around your steps and other views in the checkout workflow option in order to Display the fields where you want.
But you won't be able to display some of them here, and the rest there.