Clone and object editing

I’m new to pimcore and I would like to know if it was possible to copy an object to a different folder and when I edit the new object the other one is edited too? and its variants too?

It’s not possible ootb and I wouldn’t recommend it. It’s better if you have single copy of your data.
If you want to display single object in multiple places (e.g. to show products as a children of their categories), you can override controller which fetches the children on the tree.