Thank you for your post.
Q: 1. Copy product category assignment from another product. So for example i can add a product to same categories as another product is.
A: The Store Manager has an Assign Category Feature, allowing to select products and assign them to the same categories.
Q: 2. Add product to all categories at once.
A: Yes, the same principle in the Assign Category dialog: http://screencast.com/t/vubQwZ1TLgi
Q: 3. Add product to all third level categories.
Example: i have following category tree BMW (lv 1) -> 300 (lv 2) -> year 1998 (lv 3). And i need products in lv 3 category and not in lv 1 and 2. A: Yes, you can assign a product to the category of any depth level.
Q: 4. When i add new categories then product that is assigned to all categories would be automatically in new category as well.
A: No, product should be assigned manually to a newly created categories.
You're welcome to request a free trial of the Store Manager for PrestaShop here: