Yes, you can have more than one tree in your Family Echo account. To see the list of trees, or add another one, please use 'My Account' in the top right of the page.
I'm afraid it is not possible to copy part of a tree. You could export and import the whole tree and save it to your account as a copy, and then start with that. It really depends how much information you want from the starting tree and how much you would have to delete.
