Render Selected Area or Move layers to other comp

hi . i want to render the animated logo in my composition

first i create new Comp and try to copy and paste related layers of my logo from Comp to new smaller comp ( 200*200)

i dont know why but when i do this my logo scale in some wrong size !! 

and i dont want it , i want the size of logo or object not change after paste to my new comp

what can i do about this ?

whats the best and standard way to copy layers from one comp to another comp ( 2 comp with different sizes )

i though about using some way to render a selected area of my comp , for example 200*200 pixels or 1280*720 project but i cant find out how in google searching and i dont know that possible at all or not ?

what do you recomended for me ?  thanks